Question 1: Palette 1/192

Allen MCQ

A stationary magnet does not interact with :

A

iron rod

B

moving charge

C

moving magnet

D

stationary charge

Question 2: Palette 2/192

Allen MCQ

Figure shows a square shape loop, whose one arm BC produces magnetic field B at the centre of coil. The resultant magnetic field due to all the arms will be :-

A

4B

B

B/2

C

B

D

2B

Question 3: Palette 3/192

Allen MCQ

A wire is parallel to one arm of a square current carrying loop, which also carries current. Now at any point A within the coil the magnetic field will be :-

A

less than the magnetic field produced due to loop only.

B

more than the magnetic field produced due to loop only.

C

equal to the earlier.

D

zero

Question 4: Palette 4/192

Allen MCQ

A current of 10 A is established in a long wire along positive z-direction. The magnetic field B at the point (1m, 0, 0) is:

A

$1\mu \mathrm{T}$ along the -y direction

B

$2\mu \mathrm{T}$ along the +y direction

C

$1\mu \mathrm{T}$ along the -x direction

D

$2\mu \mathrm{T}$ along the +x direction

Question 5: Palette 5/192

Allen MCQ

Radius of current carrying coil is 'R'. Then ratio of magnetic fields at the centre of the coil to the axial point, which is $R\sqrt{3}$ distance away from the centre of the coil:-

A

1:1

B

1:2

C

1:4

D

8:1

Question 6: Palette 6/192

Allen MCQ

A coil of one loop is made by a wire of length L and there after a coil of two loops is made by same wire. The ratio of magnetic field at the centre of coils respectively:-

A

1:4

B

1:1

C

1:8

D

4:1

Question 7: Palette 7/192

Allen MCQ

Magnetic field at point O will be :-

A

$\frac{\mu_0\mathrm{I}}{2\mathrm{R}}\otimes$

B

$\frac{\mu_0\mathrm{I}}{2\mathrm{R}}\odot$

C

$\frac{\mu_0\mathrm{I}}{2\mathrm{R}}\left(1 - \frac{1}{\pi}\right)\otimes$

D

$\frac{\mu_0\mathrm{I}}{2\mathrm{R}}\left(1 + \frac{1}{\pi}\right)\odot$

Question 8: Palette 8/192

Allen MCQ

The vector form of Biot savart law for a current carrying element is :-

A

$\mathrm{d}\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{id}\ell\sin\phi}{\mathrm{r}^2}$

B

$\mathrm{d}\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{i}\vec{\mathrm{d}}\ell\times\hat{\mathrm{r}}}{\mathrm{r}^2}$

C

$\mathrm{d}\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{i}\vec{\mathrm{d}}\ell\times\hat{\mathrm{r}}}{\mathrm{r}^3}$

D

$\mathrm{d}\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{i}\vec{\mathrm{d}}\ell\times\vec{\mathrm{r}}}{\mathrm{r}^2}$

Question 9: Palette 9/192

Allen MCQ

A and B are two concentric circular loop carrying current $i_{1}$ and $i_{2}$ as shown in figure. If ratio of their radii is 1:2 and ratio of the flux densities at the centre O due to A and B is 1:3 then the value of $\frac{i_{1}}{i_{2}}$ will be :-

A

$\frac{1}{2}$

B

$\frac{1}{3}$

C

$\frac{1}{4}$

D

$\frac{1}{6}$

Question 10: Palette 10/192

Allen MCQ

For the given current distribution the magnetic field at point, 'P' is :-

A

$\frac{\mu_0}{4\pi}\odot$

B

$\frac{\mu_0}{\pi}\otimes$

C

$\frac{\mu_0}{2\pi}\otimes$

D

$\frac{\mu_0}{2\pi}\odot$

Question 11: Palette 11/192

Allen MCQ

1A current flows through an infinitely long straight wire. The magnetic field produced at a point 1m. away from it is:-

A

$2 \times 10^{-3} \mathrm{T}$

B

$\frac{2}{10} \mathrm{T}$

C

$2 \times 10^{-7} \mathrm{T}$

D

$2 \pi \times 10^{-6} \mathrm{T}$

Question 12: Palette 12/192

Allen MCQ

Two infinite long parallel wires carry equal currents in same direction. The magnetic field at mid point between the two wires is:-

A

Twice the magnetic field produced due to each of the wires

B

Half of the magnetic field produced due to each of the wires

C

Square of the magnetic field produced due to each of the wires

D

Zero

Question 13: Palette 13/192

Allen MCQ

A closely wound flat circular coil of 25 turns of wire has diameter of 10 cm and carries a current of 4 ampere. Determine the magnetic flux density at the centre of the coil:-

A

$1.679 \times 10^{-5} \mathrm{T}$

B

$2.028 \times 10^{-4} \mathrm{T}$

C

$1.257 \times 10^{-3} \mathrm{T}$

D

$1.512 \times 10^{-6} \mathrm{T}$

Question 14: Palette 14/192

Allen MCQ

$\pi$ ampere current is flowing through a long straight wire. Due to this a field of $5 \times 10^{-5}$ T produced, then distance of the point from the axis of the wire is :-

A

$10^{4}\mu_{0}\mathrm{m}$

B

$10^{5}\mu_{0}\mathrm{m}$

C

$10^{6}\mu_{0}\mathrm{m}$

D

$10^{8}\mu_{0}\mathrm{m}$

Question 15: Palette 15/192

Allen MCQ

Radius of a current carrying coil is 'R'. The ratio of magnetic field at a axial point which is R distance away from the centre of the coil to the magnetic field at the centre of the coil :-

A

$\left(\frac{1}{2}\right)^{1/2}$

B

$\frac{1}{2}$

C

$\left(\frac{1}{2}\right)^{3/2}$

D

$\frac{1}{4}$

Question 16: Palette 16/192

Allen MCQ

When the current flowing in a circular coil is doubled and the number of turns of the coil in it is halved, the magnetic field at its centre will become :-

A

Same

B

Four times

C

Half

D

Double

Question 17: Palette 17/192

Allen MCQ

Which of the following statement is not true; magnetic field at the centre of current carrying loop :-

A

proportional to current

B

inversely proportional to radius

C

proportional to number of turns

D

none

Question 18: Palette 18/192

Allen MCQ

A circular coil of radius R carries an electric current. The magnetic field due the coil at a point on the axis of the coil located at a distance r from the center of the coil, such that r >> R varies as:

A

1/r

B

$1 / \mathrm{r}^{3/2}$

C

$1 / \mathrm{r}^2$

D

$1 / \mathrm{r}^3$

Question 19: Palette 19/192

Allen MCQ

Two concentric circular loops of radii 0.08m and 0.1m carries current such that magnetic field at the centre is zero. If the current in the outer loop is 8A clockwise, current in the inner loop is :-

A

6.4 A anticlockwise

B

6.4 A clockwise

C

8A anticlockwise

D

3.2 A clockwise

Question 20: Palette 20/192

Allen MCQ

In the shown figure magnetic field at point A will be :-

A

$\frac{\mu_0\mathrm{I}}{4\pi}$

B

$\frac{\mu_0\mathrm{I}}{4\mathrm{R}}$

C

$\frac{\mu_0\mathrm{I}}{4\pi\mathrm{R}}$

D

Zero

Question 21: Palette 21/192

Allen MCQ

If radius of coil becomes two times and current becomes half then magnetic field at centre of the coil will be :-

A

Two times

B

Four times

C

Half

D

One fourth

Question 22: Palette 22/192

Allen MCQ

2A current is flowing in a circular loop of radius $1\mathrm{m}$ . Magnitude of magnetic field at the centre of circular loop will be :-

A

$\frac{\mu_0}{2}$

B

$2\mu_0$

C

$\mu_0$

D

$\frac{\mu_0}{2\pi}$

Question 23: Palette 23/192

Allen MCQ

A horizontal overhead powerline is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is :-

A

$2.5 \times 10^{-7}\mathrm{T}$ , southward

B

$5 \times 10^{-6}\mathrm{T}$ , northward

C

$5 \times 10^{-6}\mathrm{T}$ , southward

D

$2.5 \times 10^{-7}\mathrm{T}$ , northward

Question 24: Palette 24/192

Allen MCQ

The wire in the figure carries a current i and consists of a circular arc of radius R and central angle $\frac{\pi}{2}$ rad, and two straight sections whose extensions intersect the centre C of the arc. The magnetic field $\vec{B}$ that the current produces at C is :-

A

$\left|\vec{B}\right|=\frac{\mu_{0}i}{8R}$ into the plane of the figure

B

$\left|\vec{B}\right|=\frac{\mu_{0}i}{8R}$ out of the plane of the figure

C

$\left|\vec{B}\right|=\frac{\mu_{0}i}{8\pi R}$ into the plane of the figure

D

$\left|\vec{B}\right|=\frac{\mu_{0}i}{8\pi R}$ out of the plane of the figure

Question 25: Palette 25/192

Allen MCQ

For the hollow thin cylindrical current carrying pipe which statement is correct: -

A

magnetic field inside the pipe is not zero

B

magnetic field outside the pipe is zero

C

electric field outside the pipe is zero

D

electric field on the surface of pipe is zero

Question 26: Palette 26/192

Allen MCQ

In a current carrying long solenoid the field produced does not depend on :-

A

number of turns per unit length

B

current in solenoid

C

radius of cross section of the solenoid

D

all of the above

Question 27: Palette 27/192

Allen MCQ

If length and number of turns becomes half for a solenoid then value of magnetic field becomes:-

A

twice

B

same

C

half

D

one fourth

Question 28: Palette 28/192

Allen MCQ

If number of turns and current become double for any solenoid, then value of magnetic field becomes :-

A

twice

B

same

C

half

D

four times

Question 29: Palette 29/192

Allen MCQ

A current of $1/4\pi$ ampere is flowing through a toroid. It has 1000 number of turn per meter then value of magnetic field (in Wb/m $^{2}$ ) along its axis is :-

A

$10^{-2}$

B

$10^{-3}$

C

$10^{-4}$

D

$10^{-7}$

Question 30: Palette 30/192

Allen MCQ

Mean radius of a toroid is 10 cm and number of turns are 500. If current flowing through it is 0.1 ampere then value of magnetic field (in tesla) for toroid :-

A

$10^{-2}$

B

$10^{-5}$

C

$10^{-3}$

D

$10^{-4}$

Question 31: Palette 31/192

Allen MCQ

A long solenoid has length L, average diameter D and n layer of turns. Each layer contains N turns. If current flowing through the solenoid is i the value of magnetic field at the centre :-

A

Proportional to D

B

Inversely proportional to D

C

Does not depend on D

D

Proportional to L

Question 32: Palette 32/192

Allen MCQ

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of the magnetic field is:

A

B/2

B

B

C

2B

D

4B

Question 33: Palette 33/192

Allen MCQ

A long solenoid having 200 turns/cm and carries current i. Magnetic field at its axis is $6 \cdot 28 \times 10^{-2} \mathrm{~wb} / \mathrm{m}^2$ . An another solenoid having 100 turns/cm and carries $\frac{\mathrm{i}}{3}$ current, then magnetic field at its axis will be :-

A

$1.05 \times 10^{-4} \mathrm{~Wb} / \mathrm{m}^2$

B

$1.05 \times 10^{-2} \mathrm{~Wb} / \mathrm{m}^2$

C

$1.05 \times 10^{-5} \mathrm{~Wb} / \mathrm{m}^2$

D

$1.05 \times 10^{-3} \mathrm{~Wb} / \mathrm{m}^2$

Question 34: Palette 34/192

Allen MCQ

A proton and an alpha particle are separately projected in a region where a uniform magnetic field exists. The initial velocities are perpendicular to the direction of magnetic field. If both the particles move along circles of equal radii, the ratio of momentum of proton to alpha particle $\left(\frac{P_{p}}{P_{\alpha}}\right)$ is :-

A

1

B

1/2

C

2

D

1/4

Question 35: Palette 35/192

Allen MCQ

Cathode rays are moving between the poles of a magnet. Due to the effect of magnetic field of magnet :-

A

velocity of rays increases

B

velocity of rays decreases

C

rays deflected towards south pole

D

rays deflected in upward direction and perpendicular to the plane of the paper

Question 36: Palette 36/192

Allen MCQ

Following charge has maximum frequency of rotation in uniform transverse magnetic field :

A

a proton

B

an alpha particle

C

an electron

D

a neutron

Question 37: Palette 37/192

Allen MCQ

Which of the following particle will experiences maximum magnetic force, when projected with the same velocity perpendicular to a magnetic field :-

A

electron

B

proton

C

$\mathrm{He^{+}}$

D

$\mathrm{Li^{++}}$

Question 38: Palette 38/192

Allen MCQ

When $\alpha$ and $\beta$ rays are subjected to a magnetic field which is perpendicular to the direction of their motion, with their same speed. The curvature of path of both the particles are :-

A

equal

B

more for $\alpha$ particles

C

more for $\beta$ particles

D

none

Question 39: Palette 39/192

Allen MCQ

Two identically charged particles A and B initially at rest, are accelerated by a common potential difference V. They enters into a uniform transverse magnetic field B and describe a circular path of radii $r_{1}$ and $r_{2}$ respectively then their mass ratio is :-

A

$\left(\frac{r_{1}}{r_{2}}\right)^{2}$

B

$\left(\frac{r_{2}}{r_{1}}\right)^{2}$

C

$\left(\frac{r_{1}}{r_{2}}\right)$

D

$\left(\frac{r_{2}}{r_{1}}\right)$

Question 40: Palette 40/192

Allen MCQ

An $\alpha$ -particle experiences a force of $3.84 \times 10^{-14} \mathrm{~N}$ when it moves perpendicular to magnetic field of $0.2 \mathrm{~Wb} / \mathrm{m}^2$ then speed of the $\alpha$ -particle is:

A

$6.0 \times 10^{5} \mathrm{~m} / \mathrm{sec}$

B

$5.0 \times 10^{5} \mathrm{~m} / \mathrm{sec}$

C

$1.2 \times 10^{6} \mathrm{~m} / \mathrm{sec}$

D

$3.8 \times 10^{6} \mathrm{~m} / \mathrm{sec}$

Question 41: Palette 41/192

Allen MCQ

If an electron enters a magnetic field with its velocity pointing in the same direction as the magnetic field then:-

A

the electron will turn towards right

B

the electron will turn towards left

C

the velocity of the electron will increase

D

the velocity of the electron will increase

Question 42: Palette 42/192

Allen MCQ

A charge having q/m equal to $10^{8}$ C/kg and with velocity $3 \times 10^{5}$ m/s enters into a uniform magnetic field B = 0.3T at an angle $30^{\circ}$ with direction of field. Then radius will be :-

A

0.01 cm

B

0.5 cm

C

1 cm

D

2 cm

Question 43: Palette 43/192

Allen MCQ

When a charged particle enters in a uniform magnetic field its kinetic energy:-

A

remains constant

B

increases

C

decreases

D

becomes zero

Question 44: Palette 44/192

Allen MCQ

Two particles x and y have equal charges and possessing equal kinetic energy enter in a uniform magnetic field and describe circular path of radius of curvature $r_{1}$ and $r_{2}$ respectively. The ratio of their masses is:

A

$\left(\frac{r_{1}}{r_{2}}\right)$

B

$\left(\frac{r_{1}}{r_{2}}\right)^{1/2}$

C

$\left(\frac{r_{1}}{r_{2}}\right)^{2}$

D

$\left(\frac{r_{2}}{r_{1}}\right)$

Question 45: Palette 45/192

Allen MCQ

An electron having mass 'm' and kinetic energy E enter in uniform magnetic field B perpendicularly, then its frequency of uniform circular motion will be :-

A

$\frac{\mathrm{eE}}{\mathrm{qVB}}$

B

$\frac{2\pi\mathrm{m}}{\mathrm{eB}}$

C

$\frac{\mathrm{eB}}{2\pi\mathrm{m}}$

D

$\frac{2\mathrm{m}}{\mathrm{eBE}}$

Question 46: Palette 46/192

Allen MCQ

In a mass spectrograph an ion A of mass number 24 and charge +e and an ion B of mass number 22 and charge +2e are entered in transverse magnetic field with same velocity. The ratio of radii of their paths respectively:-

A

$\frac{11}{24}$

B

$\frac{12}{11}$

C

$\frac{11}{22}$

D

$\frac{24}{11}$

Question 47: Palette 47/192

Allen MCQ

A charge particle is moving in the direction of a magnetic field. The magnetic force acting on the particle :-

A

is in the direction of its velocity

B

is in the direction opposite to its velocity

C

is perpendicular to its velocity

D

is zero

Question 48: Palette 48/192

Allen MCQ

An electron of kinetic energy of $7.2 \times 10^{-18}$ J is revolving in a circular path in magnetic field $9 \times 10^{-5}$ Wb/m $^{2}$ then radius of its circular path is:-

A

1.25 cm.

B

2.5 m.

C

2.5 cm.

D

25.0 cm.

Question 49: Palette 49/192

Allen MCQ

An electron moves with velocity v in uniform transverse magnetic field B on circular path of radius 'r', then e/m for it is :-

A

$\frac{\mathrm{v}}{\mathrm{Br}}$

B

$\frac{\mathrm{B}}{\mathrm{rv}}$

C

Bvr

D

$\frac{\mathrm{vr}}{\mathrm{B}}$

Question 50: Palette 50/192

Allen MCQ

A proton, deutron and an $\alpha$ -particle are accelerated by same potential, enter in uniform magnetic field perpendicularly. Ratio of radii of circular path respectively:-

A

$1:\sqrt{2}:\sqrt{2}$

B

$2:2:1$

C

$1:2:1$

D

$1:1:1$

Question 51: Palette 51/192

Allen MCQ

A charged particle moves through a magnetic field in a direction perpendicular to it. Then the :-

A

speed of the particle remains unchanged

B

direction of motion of particle remains unchanged

C

acceleration of particle remains unchanged

D

velocity of particle remains unchanged

Question 52: Palette 52/192

Allen MCQ

A magnetic field :-

A

Always exerts a force on charged particle

B

Never exerts a force on charged particle

C

Exert a force, if the charged particle is moving across the magnetic field line

D

Exerts a force, if the charged particle is moving along the magnetic field line

Question 53: Palette 53/192

Allen MCQ

A proton and an $\alpha$ -particle moving with the same velocity and enter into a uniform magnetic field which is acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and $\alpha$ -particle respectively:-

A

$1:2$

B

$1:4$

C

$1:16$

D

$4:1$

Question 54: Palette 54/192

Allen MCQ

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity $\vec{v}$ , as shown, the magnetic force on the charge is:-

A

along ox

B

opposite to oy

C

along oy

D

opposite to ox

Question 55: Palette 55/192

Allen MCQ

In Thomson mass spectrograph $\vec{E} \perp \vec{B}$ then the velocity of undeflected electron beam will be :-

A

$\frac{|\vec{E}|}{|\vec{B}|}$

B

$\vec{E} \times \vec{B}$

C

$\frac{|\vec{B}|}{|\vec{E}|}$

D

$\frac{E^{2}}{B^{2}}$

Question 56: Palette 56/192

Allen MCQ

A charge 'q' moves in a region where electric field and magnetic field both exist, then force on it :-

A

$q(\vec{v} \times \vec{B})$

B

$q\vec{E} + q(\vec{v} \times \vec{B})$

C

$q\vec{E} + q(\vec{B} \times \vec{v})$

D

$q\vec{B} + q(\vec{E} \times \vec{v})$

Question 57: Palette 57/192

Allen MCQ

An electric field E and a magnetic field B applied on a proton which moves with velocity v, it goes undeflected through the region if :-

A

$\mathrm{E} \perp \mathrm{B}$

B

E is parallel to v and perpendicular to B

C

E, B and v all three mutually perpendicular to each other and $v = E / B$

D

E and B both are parallel but perpendicular to v

Question 58: Palette 58/192

Allen MCQ

In a region constant uniform electric and magnetic field is present. Both field are parallel. In this region a charge released from rest, then path of particle is :-

A

Circle

B

Helical

C

Straight line

D

Ellipse

Question 59: Palette 59/192

Allen MCQ

A wire PQ carries a current 'i' is placed perpendicular to a long wire XY carrying a current I. The direction of force on PQ will be:-

A

towards right

B

towards left

C

upwards

D

downwards

Question 60: Palette 60/192

Allen MCQ

A current carrying wire AC is placed in uniform transverse magnetic field then the force on wire AC :-

A

3N

B

4.2N

C

6N

D

4N

Question 61: Palette 61/192

Allen MCQ

Force exist on a current carrying wire which is placed in external magnetic field, due to :-

A

free electrons in wire

B

free positive ions in wire

C

1) & 2) both

D

none

Question 62: Palette 62/192

Allen MCQ

P, Q and R long parallel straight wires in air, carrying currents as shown. The direction of resultant force on R is :-

A

towards left

B

towards right

C

the same as that of current in Q

D

perpendicular to plane of paper

Question 63: Palette 63/192

Allen MCQ

Two parallel wires in free space are 10 cm apart and each carries a current of 10 A in the same direction. The magnetic force per unit length of each wire is :-

A

$2 \times 10^{-4}\mathrm{N}$ , attractive

B

$2 \times 10^{-4}\mathrm{N}$ , repulsive

C

$2 \times 10^{-7}\mathrm{N}$ , attractive

D

$2 \times 10^{-7}\mathrm{N}$ , repulsive

Question 64: Palette 64/192

Allen MCQ

Wire in the form of a right angle ABC, with AB=3cm and BC = 4cm, carries a current of 10A. There is a uniform magnetic field of 5T perpendicular to the plane of the wire. The force on the wire will be :-

A

1.5N

B

2.0N

C

2.5N

D

3.5N

Question 65: Palette 65/192

Allen MCQ

When direct current passed through a spring then it :-

A

Contracts

B

Expands

C

Vibrate

D

Unchange

Question 66: Palette 66/192

Allen MCQ

A rectangular loop carrying a current $i_{1}$ , is situated near a long straight wire carrying a steady current $i_{2}$ . The wire is parallel to one of the sides of the loop and is in the plane of the loop as shown in the figure. Then the current loop will :-

A

move away from the wire

B

move towards the wire.

C

remain stationary.

D

rotate about an axis parallel to the wire.

Question 67: Palette 67/192

Allen MCQ

A current carrying wire is arranged at any angle in an uniform magnetic field, then

A

only force acts on wire

B

only torque acts on wire

C

both

D

none

Question 68: Palette 68/192

Allen MCQ

Two parallel beams of positrons moving in the same direction will :-

A

Repel to each other

B

Will not interact with each other

C

Attract to each other

D

Be deflected normal to the plane containing the two beams

Question 69: Palette 69/192

Allen MCQ

Due to the flow of current in a circular loop of radius R, the magnetic field produced at the centre of the loop is B. The magnetic moment of the loop is :-

A

$BR^{3}/2\pi\mu_{0}$

B

$2\pi BR^{3}/\mu_{0}$

C

$BR^{2}/2\pi\mu_{0}$

D

$2\pi BR^{2}/\mu_{0}$

Question 70: Palette 70/192

Allen MCQ

A circular loop has a radius of 5 cm. and it is carrying a current of 0.1 A. its magnetic moment is:-

A

$1.32 \times 10^{-4}$ amp- $m^{2}$

B

$2.62 \times 10^{-4}$ amp- $m^{2}$

C

$5.25 \times 10^{-4}$ amp- $m^{2}$

D

$7.85 \times 10^{-4}$ amp- $m^{2}$

Question 71: Palette 71/192

Allen MCQ

An electron is moving in a circle of radius $5.1 \times 10^{-11}$ m at a frequency of $6.8 \times 10^{15}$ rev./sec. The equivalent current is approximately:

A

$5.1 \times 10^{-3}$ A

B

$6.8 \times 10^{-3}$ A

C

$1.1 \times 10^{-3}$ A

D

$2.2 \times 10^{-3}$ A

Question 72: Palette 72/192

Allen MCQ

If number of turn, area and current through the coil is given by n, A and i respectively then its magnetic moment will be :-

A

niA

B

$n^{2}iA$

C

$niA^{2}$

D

$\frac{ni}{\sqrt{A}}$

Question 73: Palette 73/192

Allen MCQ

An electron is moving around a proton in an orbit of radius 1Å and produces 16 Wb/m² of magnetic field at the centre, then find the angular velocity of electron :

A

$20 \pi \times 10^{16}$ rad/sec

B

$10 \times 10^{16}$ rad/sec

C

$\frac{5}{2\pi} \times 10^{16}$ rad/sec

D

$\frac{5}{4\pi} \times 10^{16}$ rad/sec

Question 74: Palette 74/192

Allen MCQ

Current I is flowing in a conducting circular loop of radius R. It is kept in a magnetic field B which is perpendicular to the plane of circular loop, the magnetic force acting on the loop is :-

A

IRB

B

$2\pi$ IRB

C

Zero

D

$\pi$ IRB

Question 75: Palette 75/192

Allen MCQ

The unit of magnetic moment will be :-

A

$\frac{A}{m}$

B

$A - m^{2}$

C

$\frac{T - m}{A}$

D

$\frac{T - m}{A^{2}}$

Question 76: Palette 76/192

Allen MCQ

A current carrying coil behave like tiny magnet. If area of coil is A and magnetic moment is 'M' then current through the coil is :-

A

$\frac{\mathrm{M}}{\mathrm{A}}$

B

$\frac{\mathrm{A}}{\mathrm{M}}$

C

MA

D

$\frac{\mathrm{A}^2}{\mathrm{M}}$

Question 77: Palette 77/192

Allen MCQ

An electron revolves with frequency $6.6 \times 10^{15}$ r.p.s. around nucleus in circular orbit of radius 0.53 Å of hydrogen atom, then magnetic field produced at centre of orbit is:

A

0.125 T

B

1.25 T

C

12.5 T

D

125 T

Question 78: Palette 78/192

Allen MCQ

A current loop of area $0.01m^{2}$ and carrying a current of 10A is held perpendicular to a magnetic field of 0.1T, the torque in N-m acting on the loop is :-

A

0

B

0.001

C

0.01

D

1.1

Question 79: Palette 79/192

Allen MCQ

A current carrying coil is placed in a constant uniform magnetic field B. Torque is maximum on this coil when plane of coil is :-

A

perpendicular to B

B

parallel to B

C

at $45^{\circ}$ to B

D

at $60^{\circ}$ to B

Question 80: Palette 80/192

Allen MCQ

Magnetic field is parallel to the plane of coil then torque will be :-

A

Maximum

B

Minimum

C

Zero

D

None of these

Question 81: Palette 81/192

Allen MCQ

The work done in rotating a magnet of magnetic moment M by an angle of $90^{\circ}$ from the external magnetic field direction is 'n' times the corresponding work done to turn it through an angle of $60^{\circ}$ . Where 'n' gives by:

A

1/2

B

2

C

1/4

D

1

Question 82: Palette 82/192

Allen MCQ

Magnetic field lines produced by a bar magnet, cuts each other :-

A

At neutral points

B

Near the poles of the magnets

C

At equatorial axis

D

Never intersects to each other

Question 83: Palette 83/192

Allen MCQ

For protecting a magnetic needle it should be placed :-

A

in an iron box

B

in wooden box

C

in metallic box

D

none of these

Question 84: Palette 84/192

Allen MCQ

Which of the following materials is repelled by an external magnetic field :-

A

Iron

B

Cobalt

C

Steel

D

Copper

Question 85: Palette 85/192

Allen MCQ

If a diamagnetic material is placed in a magnetic field, the flux density inside the material compared to that outside will be:

A

Slightly less

B

Slightly more

C

Very much more

D

Same

Question 86: Palette 86/192

Allen MCQ

To protect a sensitive instrument from external magnetic jerks, it should be placed in a container made of :-

A

Nonmagnetic substance

B

Diamagnetic substance

C

Paramagnetic substance

D

Ferromagnetic substance

Question 87: Palette 87/192

Allen MCQ

Substances in which the magnetic moment of a single atom is not zero, are known as :

A

Diamagnetic

B

Ferromagnetic

C

Paramagnetic

D

2) and 3) both

Question 88: Palette 88/192

Allen MCQ

Susceptibility of a magnetic substance is found to depend on temperature and the strength of the magnetising field. The material is a :-

A

Diamagnetic

B

Ferromagnetic

C

Paramagnetic

D

Superconductor

Question 89: Palette 89/192

Allen MCQ

Property possessed by only ferromagnetic substance is :-

A

Attracting magnetic substance

B

Hysteresis

C

Susceptibility independent of temperature

D

Directional property

Question 90: Palette 90/192

Allen MCQ

The hard ferromagnetic material is characterized by:-

A

Narrow hysteresis loop

B

Broad hysteresis loop

C

High mechanically hardness, all over

D

Mechanically hard surface

Question 91: Palette 91/192

Allen MCQ

The magnetic moment of paramagnetic materials is :-

A

Infinity

B

Zero

C

Constant but low

D

None of above

Question 92: Palette 92/192

Allen MCQ

The cause of paramagnetism is:

A

Unparied electrons

B

Electron excess and spin motion of electrons

C

Paired electrons and orbital motion of electrons

D

Electrons and orbital motion of electrons

Question 93: Palette 93/192

Allen MCQ

The cause of diamagnetism is :-

A

Orbital motion of electrons

B

Spin motion of electrons

C

Paired electrons

D

None of the above

Question 94: Palette 94/192

Allen MCQ

The magnetic moment of diamagnetic materials is :-

A

Infinity

B

Zero

C

$100\mathrm{amp - m^2}$

D

None of the above

Question 95: Palette 95/192

Allen MCQ

Which of the following statements is correct for diamagnetic materials :-

A

$\mu_{\mathrm{r}} < 1$

B

$\chi$ is negative and low

C

$\chi$ does not depend on temperature

D

All of the above

Question 96: Palette 96/192

Allen MCQ

The area of B-H loop for soft iron, as compared to that for steel is :-

A

More

B

Less

C

Equal

D

None of the above

Question 97: Palette 97/192

Allen MCQ

The liquid in the watch glass in the following figure is -

A

Ferromagnetic

B

Paramagnetic

C

Diamagnetic

D

Nonmagnetic

Question 98: Palette 98/192

Allen MCQ

Powerful permanent magnets are made of :-

A

Cobalt

B

Aluminum

C

Tin-coal

D

Cobalt-steel

Question 99: Palette 99/192

Allen MCQ

Which of the following statements is correct for ferromagnetic material :-

A

These become diamagnetic at Curie temperature

B

These become paramagnetic at Curie temperature

C

Their magnetic susceptibility becomes zero at Curie temperature

D

Its magnetic properties are explained on
the basis of electron principle

Question 100: Palette 100/192

Allen MCQ

A material rod, when placed in a strong magnetic field, aligns itself at right angles to the magnetic field. The nature of material is :-

A

Diamagnetic

B

Paramagnetic

C

Ferromagnetic

D

Low ferromagnetic

Question 101: Palette 101/192

Allen MCQ

The relative permeability of air is:

A

Zero

B

1.04

C

Infinity

D

1

Question 102: Palette 102/192

Allen MCQ

If the magnetic susceptibility of a magnetic material is -0.004 then its nature will be :-

A

Diamagnetic

B

Paramagnetic

C

Ferromagnetic

D

Non magnetic

Question 103: Palette 103/192

Allen MCQ

The correct measure of magnetic hardness of a material is :-

A

Remanent magnetism

B

Hysteresis loss

C

Coercivity

D

Curie temperature

Question 104: Palette 104/192

Allen MCQ

If the relative permeability of a material is 0.9999 then its nature will be :-

A

Paramagnetic

B

Diamagnetic

C

Ferromagnetic

D

Non-magnetic

Question 105: Palette 105/192

Allen MCQ

The magnetic susceptibility of a paramagnetic material at $-73^{\circ}C$ is 0.0075 then its value at $-173^{\circ}C$ will be :-

A

0.0045

B

0.0030

C

0.015

D

0.0075

Question 106: Palette 106/192

Allen MCQ

When a magnetic substance is heated, then it:

A

Becomes a strong magnet

B

Losses its magnetism

C

Does not effect the magnetism

D

Either (1) or (3)

Question 107: Palette 107/192

Allen MCQ

Diamagnetic substance are :-

A

Feebly attracted by magnets

B

Strongly attracted by magnets

C

Feebly repelled by magnets

D

Strongly repelled by magnets

Question 108: Palette 108/192

Allen MCQ

If a diamagnetic solution is poured into a U-tube and one arm of this U-tube placed between the poles of a strong magnet with the meniscus in a line with the field, then the level of the solution will :-

A

Rise

B

Fall

C

Oscillate slowly

D

Remain as such

Question 109: Palette 109/192

Allen MCQ

Magnetic permeability is maximum for :

A

Diamagnetic substance

B

Paramagnetic substance

C

Ferromagnetic substance

D

All of these

Question 110: Palette 110/192

Allen MCQ

Which one of the following is ferro-magnetic:-

A

Co

B

Zn

C

Hg

D

Pt

Question 111: Palette 111/192

Allen MCQ

For paramagnetic materials magnetic susceptibility is related with temperature as:

A

$\propto$ T $^{2}$

B

$\propto$ T $^{1}$

C

$\propto$ T $^{-1}$

D

$\propto$ T $^{-2}$

Question 112: Palette 112/192

Allen MCQ

According to Curie's law, the magnetic susceptibility of a substance at an absolute temperature T is proportional to:

A

1/T

B

T

C

$1 / \mathrm{T}^2$

D

$\mathrm{T}^2$

Question 113: Palette 113/192

Allen MCQ

A diamagnetic material in a magnetic field moves

A

from stronger to the weaker parts of the field

B

from weaker to the stronger parts of the field

C

perpendicular to the field

D

in none of the above directions

Question 114: Palette 114/192

Allen MCQ

Diamagnetic substances characterise by :-

A

low and negative magnetic susceptibility

B

low and positive magnetic susceptibility

C

high and negative magnetic susceptibility

D

high and positive magnetic susceptibility

Question 115: Palette 115/192

Allen MCQ

Magnetic susceptibility of a diamagnetic substance varies with absolute temperature as :-

A

directly proportional to T

B

inversely proportional to T

C

remains unchanged with T

D

exponential decrease with T

Question 116: Palette 116/192

Allen MCQ

The material of permanent magnet has

A

High retentivity, low coercivity

B

Low retentivity, high coercivity

C

Low retentivity, low coercivity

D

High retentivity, high coercivity

Question 117: Palette 117/192

Allen MCQ

Hysteresis property is shown by :-

A

paramagnetic and diamagnetic

B

diamagnetic

C

paramagnetic

D

ferromagnetic

Question 118: Palette 118/192

Allen MCQ

Magnetic susceptibility of the following is :

A

negative for diamagnetic

B

positive for diamagnetic and paramagnetic

C

negative for diamagnetic and zero for paramagnetic

D

zero for paramagnetic and positive for ferromagnetic

Question 119: Palette 119/192

Allen MCQ

Which statement is true:

A

atomic magnetic dipole moment of diamagnet is zero

B

atomic magnetic dipole moment of paramagnet is zero

C

atomic magnetic dipole moment of ferromagnet is zero

D

ferromagnet is demagnetised rapidly after moving in magnetising field.

Question 120: Palette 120/192

Allen MCQ

Curie-Weiss law is obeyed by iron at a temperature......

A

Below Curie temperature

B

Above Curie temperature

C

At Curie temperature only

D

At all temperatures

Question 121: Palette 121/192

Allen MCQ

Ferromagnetic substance contain :-

A

empty subshell

B

partially empty subshell

C

full fill subshell

D

none of these

Question 122: Palette 122/192

Allen MCQ

Soft iron is used to make the core of transformer, because of its:

A

low coercivity and low retentivity

B

low coercivity and high retentivity

C

high coercivity and high retentivity

D

high coercivity and low retentivity

Question 123: Palette 123/192

Allen MCQ

Above curie temperature ferromagnetic substance converts into:

A

paramagnetic

B

diamagnetic

C

ferromagnetic

D

non magnetic

Question 124: Palette 124/192

Allen MCQ

Relation between $\mu_{\mathrm{r}}$ and $\chi$ will be:

A

$\mu_{\mathrm{r}} = 1 + \chi$

B

$\chi = \mu_{\mathrm{r}} + 1$

C

$\frac{\mu_0}{\mu}$

D

$\mu_0\chi$

Question 125: Palette 125/192

Allen MCQ

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that 'O' is their common point for the two. The wires carry $\mathrm{I}_1$ and $\mathrm{I}_2$ currents respectively. Point 'P' is lying at distance 'd' from 'O' along a direction perpendicular to the plane containing the wires. The magnetic field at the point 'P' will be :-

A

$\frac{\mu_0}{2\pi d}\left(\frac{\mathrm{I}_1}{\mathrm{I}_2}\right)$

B

$\frac{\mu_0}{2\pi d} (\mathrm{I}_1 + \mathrm{I}_2)$

C

$\frac{\mu_0}{2\pi d} (\mathrm{I}_1^2 -\mathrm{I}_2^2)$

D

$\frac{\mu_0}{2\pi d} (\mathrm{I}_1^2 +\mathrm{I}_2^2)^{1 / 2}$

Question 126: Palette 126/192

Allen MCQ

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude:

A

Zero

B

$\frac{\mu_{0}n^{2}e}{r}$

C

$\frac{\mu_{0}ne}{2r}$

D

$\frac{\mu_{0}ne}{2\pi r}$

Question 127: Palette 127/192

Allen MCQ

A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semi-circular portion of radius R is lying in Y-Z plane. Magnetic field at point O is :

A

$\vec{\mathrm{B}} = -\frac{\mu_0}{4\pi}\frac{\mathrm{I}}{\mathrm{R}}\Bigl (\pi \hat{\mathrm{i}} -2\hat{\mathrm{k}}\Bigr)$

B

$\vec{\mathrm{B}} = -\frac{\mu_0}{4\pi}\frac{\mathrm{I}}{\mathrm{R}}\Bigl (\pi \hat{\mathrm{i}} +2\hat{\mathrm{k}}\Bigr)$

C

$\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{I}}{\mathrm{R}}\Bigl (\pi \hat{\mathrm{i}} -2\hat{\mathrm{k}}\Bigr)$

D

$\vec{\mathrm{B}} = \frac{\mu_0}{4\pi}\frac{\mathrm{I}}{\mathrm{R}}\Bigl (\pi \hat{\mathrm{i}} +2\hat{\mathrm{k}}\Bigr)$

Question 128: Palette 128/192

Allen MCQ

A rectangular coil of length 0.12m and width 0.1m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Weber/m². The coil carries a current of 2A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be:

A

0.12 Nm

B

0.15 Nm

C

0.20 Nm

D

0.24 Nm

Question 129: Palette 129/192

Allen MCQ

A proton and an alpha particle both enter a region of uniform magnetic field, B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be :-

A

1 MeV

B

4 MeV

C

0.5 MeV

D

1.5 MeV

Question 130: Palette 130/192

Allen MCQ

A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be :-

A

$\frac{2\mu_0\mathrm{Ii}}{3\pi}$

B

$\frac{\mu_0\mathrm{Ii}}{2\pi}$

C

$\frac{2\mu_0\mathrm{IiL}}{3\pi}$

D

$\frac{\mu_0\mathrm{IiL}}{2\pi}$

Question 131: Palette 131/192

Allen MCQ

The magnetic susceptibility is negative for :

A

diamagnetic material only

B

paramagnetic material only

C

ferromagnetic material only

D

paramagnetic and ferromagnetic materials

Question 132: Palette 132/192

Allen MCQ

A long straight wire of radius a carry a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B', at radial distances $\frac{a}{2}$ and 2a respectively, from the axis of the wire is:

A

$\frac{1}{4}$

B

$\frac{1}{2}$

C

1

D

4

Question 133: Palette 133/192

Allen MCQ

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be :-

A

2nB

B

$2n^2B$

C

nB

D

$n^2B$

Question 134: Palette 134/192

Allen MCQ

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by $60^{\circ}$ is W. Now the torque required to keep the magnet in this new position is:

A

$\frac{\sqrt{3}W}{2}$

B

$\frac{2W}{\sqrt{3}}$

C

$\frac{W}{\sqrt{3}}$

D

$\sqrt{3}W$

Question 135: Palette 135/192

Allen MCQ

An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57 \times 10^{-2}$ T. If the value of e/m is $1.76 \times 10^{11}$ C/kg, the frequency of revolution of the electron is :-

A

62.8 MHz

B

6.28 MHz

C

1 GHz

D

100 MHz

Question 136: Palette 136/192

Allen MCQ

A 250 turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 μA and subjected to magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is:-

A

4.55 μJ

B

2.3 μJ

C

1.15 μJ

D

9.1 μJ

Question 137: Palette 137/192

Allen MCQ

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current 'I along the same direction is shown in fig. Magnitude of force per unit length on the middle wire 'B' is given by :-

A

$\frac{2\mu_0\mathrm{i}^2}{\pi\mathrm{d}}$

B

$\frac{\sqrt{2}\mu_0\mathrm{i}^2}{\pi\mathrm{d}}$

C

$\frac{\mu_0\mathrm{i}^2}{\sqrt{2}\pi\mathrm{d}}$

D

$\frac{\mu_0\mathrm{i}^2}{2\pi\mathrm{d}}$

Question 138: Palette 138/192

Allen MCQ

A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from

A

the current source

B

the magnetic field

C

the lattice structure of the material of the rod

D

the induced electric field due to the changing magnetic field

Question 139: Palette 139/192

Allen MCQ

A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance d, from the centre of the conductor, is correctly represented by the figure :

A

B

C

D

Question 140: Palette 140/192

Allen MCQ

Ionized hydrogen atoms and $\alpha$ -particles with same momenta enters perpendicular to a constant magnetic field B. The ratio of their radii of their paths $r_{H}: r_{\alpha}$ will be

A

2:1

B

1:2

C

4:1

D

1:4

Question 141: Palette 141/192

Allen MCQ

Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry same current i, then the ratio of the magnetic fields along the two is:

A

1:1

B

4:1

C

2:1

D

1:2

Question 142: Palette 142/192

Allen MCQ

A straight conductor carrying current i splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is :

A

Zero

B

$3\mu0i/32$ R, outward

C

$3\mu0i/32R$ , inward

D

$\mu0i/2R$ , inward

Question 143: Palette 143/192

Allen MCQ

An iron rod of susceptibility 599 is subjected to a magnetising field of $1200\mathrm{A}\mathrm{m}^{-1}$ . The permeability of the material of the rod is: $(\mu_0 = 4\pi \times 10^{-7}\mathrm{TmA}^{-1})$

A

$2.4\pi \times 10^{-7}\mathrm{TmA}^{-1}$

B

$2.4\pi \times 10^{-4}\mathrm{TmA}^{-1}$

C

$8.0\times 10^{-5}\mathrm{TmA}^{-1}$

D

$2.4\pi \times 10^{-5}\mathrm{TmA}^{-1}$

Question 144: Palette 144/192

Allen MCQ

A long solenoid of 50 cm length having 100 turns carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: $(\mu_{0}=4\pi\times10^{-7}\mathrm{T}\mathrm{m}\mathrm{A}^{-1})$

A

$3.14\times10^{-5}$ T

B

$6.28\times10^{-4}$ T

C

$3.14\times10^{-4}$ T

D

$6.28\times10^{-5}$ T

Question 145: Palette 145/192

Allen MCQ

A wire of length L metre carrying a current of I ampere is bent in the form of a circle. Its magnetic moment is,

A

IL $^{2}$ /4 A m $^{2}$

B

IπL $^{2}$ /4 A m $^{2}$

C

2IL $^{2}$ /π A m $^{2}$

D

IL $^{2}$ /4π A m $^{2}$

Question 146: Palette 146/192

Allen MCQ

A thick current carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by :

A

B

C

D

Question 147: Palette 147/192

Allen MCQ

An infinitely long straight conductor carries a current of 5 A as shown. An electron is moving with a speed of $10^{5}$ m/s parallel to the conductor. The perpendicular distance between the electron and the conductor is 20 cm at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

A

$4 \times 10^{-20} \mathrm{~N}$

B

$8\pi \times 10^{-20} \mathrm{~N}$

C

$4\pi \times 10^{-20} \mathrm{~N}$

D

$8 \times 10^{-20} \mathrm{~N}$

Question 148: Palette 148/192

Allen MCQ

In the product $\vec{\mathrm{F}} = \mathrm{q}\left(\vec{\mathrm{v}} \times \vec{\mathrm{B}}\right) = \mathrm{q}\vec{\mathrm{v}} \times \left(\mathrm{B}\hat{\mathrm{i}} + \mathrm{B}\hat{\mathrm{j}} + \mathrm{B}_0\hat{\mathrm{k}}\right)$ For $q = 1$ and $\vec{\mathrm{v}} = 2\hat{\mathrm{i}} + 4\hat{\mathrm{j}} + 6\hat{\mathrm{k}}$ and $\vec{\mathrm{F}} = 4\hat{\mathrm{i}} - 20\hat{\mathrm{j}} + 12\hat{\mathrm{k}}$ What will be the complete expression for $\vec{\mathrm{B}}$ ?

A

$-8\hat{\mathrm{i}} - 8\hat{\mathrm{j}} - 6\hat{\mathrm{k}}$

B

$-6\hat{\mathrm{i}} - 6\hat{\mathrm{j}} - 8\hat{\mathrm{k}}$

C

$8\hat{\mathrm{i}} + 8\hat{\mathrm{j}} - 6\hat{\mathrm{k}}$

D

$6\hat{\mathrm{i}} + 6\hat{\mathrm{j}} - 8\hat{\mathrm{k}}$

Question 149: Palette 149/192

Allen MCQ

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side 'a'. (ii) a square of side 'a'. The magnetic dipole moments of the coil in each case respectively are:

A

$\sqrt{3}\mathrm{Ia}^2$ and $3\mathrm{Ia}^2$

B

$3\mathrm{Ia}^2$ and $\mathrm{Ia}^2$

C

$3\mathrm{Ia}^2$ and $4\mathrm{Ia}^2$

D

$4\mathrm{Ia}^2$ and $3\mathrm{Ia}^2$

Question 150: Palette 150/192

Allen MCQ

Given below are two statements: Statement I : Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element (Idl) of a current carrying conductor only. Statement II : Biot-Savart's law is analogous to Coulomb's inverse square law of charge q, with the former being related to the field produced by a scalar source, Idl while the latter being produced by a vector source, q. In light of above statement choose the most appropriate answer from the options given below:

A

Both statement I and Statement II are incorrect

B

Statement I is correct and Statement II is incorrect

C

Statement I is incorrect and Statement II is correct

D

Both statement I and Statement II are correct

Question 151: Palette 151/192

Allen MCQ

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is:

A

a linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.

B

a linearly increasing function of distance upto the boundary of the wire and then decreasing one with 1/r dependence for the outside region.

C

a linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region.

D

uniform and remains constant for both the regions.

Question 152: Palette 152/192

Allen MCQ

A closely packed coil having 1000 turns has an average radius of 62.8 cm. If current carried by the wire of the coil is 1 A, the value of magnetic field produced at the centre of the coil will be (permeability of free space = $4\pi \times 10^{-7}$ H/m) nearly:

A

$10^{-1}$ T

B

$10^{-2}$ T

C

$10^{2}$ T

D

$10^{-3}$ T

Question 153: Palette 153/192

Allen MCQ

The shape of the magnetic field lines due to an infinite long, straight current carrying conductor is:

A

a straight line

B

circular

C

elliptical

D

a plane

Question 154: Palette 154/192

Allen MCQ

Two very long, straight, parallel conductors A and B carry current of 5A and 10A respectively and are at a distance of 10 cm from each other. The direction of current in two conductors is same. The force acting per unit length between two conductors is: $(\mu_{0}=4\pi\times10^{-7}\mathrm{SI}\mathrm{unit})$

A

$2\times10^{-4}Nm^{-1}$ and is attractive

B

$2\times10^{-4}Nm^{-1}$ and is repulsive

C

$1\times10^{-4}Nm^{-1}$ and is attractive

D

$1\times10^{-4}Nm^{-1}$ and is repulsive

Question 155: Palette 155/192

Allen MCQ

The magnetic field on the axis of a circular loop of radius 100 cm carrying current $I=\sqrt{2}A$ , at point 1 m away from the centre of the loop is given by:

A

$3.14 \times 10^{-7}$ T

B

$6.28 \times 10^{-7}$ T

C

$3.14 \times 10^{-4}$ T

D

$6.28 \times 10^{-4}$ T

Question 156: Palette 156/192

Allen MCQ

The net magnetic flux through any closed surface is :

A

Positive

B

Infinity

C

Negative

D

Zero

Question 157: Palette 157/192

Allen MCQ

A wire carrying a current I along the positive x-axis has length L. It is kept in a magnetic field $\vec{\mathrm{B}} = (2\hat{\mathrm{i}} + 3\hat{\mathrm{j}} - 4\hat{\mathrm{k}})\mathrm{T}$ . The magnitude of the magnetic force acting on the wire is:

A

$\sqrt{5}$ IL

B

5 IL

C

$\sqrt{3}$ IL

D

3 IL

Question 158: Palette 158/192

Allen MCQ

A very long conducting wire is bent in a semi-circular shape from A to B as shown in figure. The magnetic field at point P for steady current configuration is given by :

A

$\frac{\mu_0\mathrm{i}}{4\mathrm{R}}$ pointed away from the page

B

$\frac{\mu_0\mathrm{i}}{4\mathrm{R}}\left[1 - \frac{2}{\pi}\right]$ pointed away from page

C

$\frac{\mu_0\mathrm{i}}{4\mathrm{R}}\left[1 - \frac{2}{\pi}\right]$ pointed into the page

D

$\frac{\mu_0\mathrm{i}}{4\mathrm{R}}$ pointed into the page

Question 159: Palette 159/192

Allen MCQ

A long straight wire of length 2 m and mass 250 g is suspended horizontally in a uniform horizontal magnetic field of 0.7 T. The amount of current flowing through the wire will be $(g = 9.8 \, \text{ms}^{-2})$ :

A

2.45 A

B

2.25 A

C

2.75 A

D

1.75 A

Question 160: Palette 160/192

Allen MCQ

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron:

A

will turn towards right of direction of motion

B

will turn towards left of direction of motion

C

speed will decrease

D

speed will increase

Question 161: Palette 161/192

Allen Match the Columns

Match Column-I(Material) with Column-II(Susceptibility( $\chi$ )). Choose the correct answer from the options given below:

Column-I	Column-II
(A) Diamagnetic (B) Ferromagnetic (C) Paramagnetic (D) Non-Magnetic	(P) $\chi = 0$ (Q) $0 > \chi \geq -1$ (R) $\chi >> 1$ (S) $0 < \chi < \varepsilon$ (a small positive number)

A

A–Q, B–R, C–S, D–P

B

A–Q, B–P, C–R, D–S

C

A–R, B–Q, C–P, D–S

D

A–S, B–R, C–Q, D–P

Question 162: Palette 162/192

Allen MCQ

In a uniform magnetic field of 0.049 T, a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6}$ kg m $^{2}$ . If the magnitude of magnetic moment of the needle is x $\times$ $10^{-5}$ Am $^{2}$ ; then the value of 'x' is :

A

$5\pi^2$

B

$128\pi^2$

C

$50\pi^2$

D

$1280\pi^2$

Question 163: Palette 163/192

Allen MCQ

A tightly wound 100 turns coil of radius $10\mathrm{cm}$ carries a current of 7 A. The magnitude of the magnetic field at the centre of the coil is (Take permeability of free space as $4\pi \times 10^{-7}$ SI units):

A

$44\mathrm{mT}$

B

$4.4\mathrm{T}$

C

$4.4\mathrm{mT}$

D

$44\mathrm{T}$

Question 164: Palette 164/192

Allen MCQ

An iron bar of length L has magnetic moment M. It is bent at the middle of its length such that the two arms make an angle $60^{\circ}$ with each other. The magnetic moment of this new magnet is:

A

M

B

$\frac{M}{2}$

C

2M

D

$\frac{M}{\sqrt{3}}$

Question 165: Palette 165/192

Allen MCQ

A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: A. hold the sheet there if it is magnetic. B. hold the sheet there if it is non-magnetic. C. move the sheet away from the pole with uniform velocity if it is conducting. D. move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar. Choose the correct statement(s) from the options given below:

A

B and D only

B

A and C only

C

A, C and D only

D

C only

Question 166: Palette 166/192

Allen MCQ

The magnetic potential energy, when a magnetic bar of magnetic moment $\vec{\mathrm{m}}$ is placed perpendicular to the magnetic field $\vec{\mathrm{B}}$ is:

A

$-\frac{\mathrm{mB}}{2}$

B

zero

C

-m B

D

m B

Question 167: Palette 167/192

Allen MCQ

The incorrect relation for a diamagnetic material (all the symbols carry their usual meaning and $\varepsilon$ is a small positive number) is:

A

$\mu < \mu_0$

B

$0 \leq \mu_r < 1$

C

$-1 \leq \chi < 0$

D

$1 < \mu_r < 1 + \varepsilon$

Question 168: Palette 168/192

Allen MCQ

The magnetic moment and moment of inertia of a magnetic needle as shown are, respectively $1.0 \times 10^{-2}$ A m $^{2}$ and $\frac{10^{-6}}{\pi^{2}}$ kg m $^{2}$ . If it completes 10 oscillations in 10 s, the magnitude of the magnetic field is :

A

$0.4\mathrm{T}$

B

$4\mathrm{T}$

C

$0.4\mathrm{mT}$

D

$4\mathrm{mT}$

Question 169: Palette 169/192

Allen MCQ

The magnetic moment of an iron bar is M. It is now bent in such a way that it forms an arc section of a circle subtending an angle of 60° at the centre. The magnetic moment of this arc section is:

A

$\frac{3M}{\pi}$

B

$\frac{4M}{\pi}$

C

$\frac{M}{\pi}$

D

$\frac{2M}{\pi}$

Question 170: Palette 170/192

Allen MCQ

Two circular coils of radii 5 cm and 10 cm carry currents of 2 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as their centres coincide. Magnitude of magnetic field at the common centre of coils is
(a) $8\pi \times 10^{-4}$ T if currents in the coils are in same sense
(b) $4\pi \times 10^{-4}$ T if currents in the coils are in opposite sense
(c) zero if currents in the coils are in opposite sense
(d) $8\pi \times 10^{-4}$ T if currents in the coils are in opposite sense

A

b and d are correct

B

a and c are correct

C

only a are correct

D

only d are correct

Question 171: Palette 171/192

Allen MCQ

When a current carrying coil is placed in a uniform magnetic field with its magnetic moment anti-parallel to the field
(a) Torque on it is maximum
(b) Torque on it is zero
(c) Potential energy is maximum
(d) Dipole is in unstable equilibrium

A

b, c, d are correct

B

only b is correct

C

a and c are correct

D

none

Question 172: Palette 172/192

Allen MCQ

If a long cylindrical conductor carries a steady current parallel to its length
(a) the electric field along the axis is zero
(b) the magnetic field along the axis is zero
(c) the magnetic field outside the conductor is zero
(d) the electric field outside the conductor is zero

A

b and d are correct

B

a and c are correct

C

only d is correct

D

none

Question 173: Palette 173/192

Allen MCQ

A charged particle revolves in circular path in uniform transverse magnetic field after being accelerated by a potential difference of V volt. If V is doubled, then choose the correct options.
(a) Kinetic energy of particle will become two times
(b) Radius of circular path will become two times
(c) Radius of circular path will become $\sqrt{2}$ times
(d) angular velocity will remain unchanged

A

a and b are correct

B

a and c are correct

C

a, c, d are correct

D

none

Question 174: Palette 174/192

Allen MCQ

abcd is a square. There is a current I in wire efg as shown. Choose the correct options :

(a) Net magnetic field at a is inwards
(b) Net magnetic field at f is zero
(c) Net magnetic field at c is zero
(d) Net magnetic field at g is zero

A

a and b are correct

B

a, b, c are correct

C

b and c are correct

D

none

Question 175: Palette 175/192

Allen MCQ

In column I, a current carrying loop and a uniform magnetic field are shown. Match this with column II.

Column-I	Column-II
(A) (B) (C) (D)	(P) F ≠ 0 (Q) Maximum torque (R) Minimum potential energy (S) Positive potential energy

A

A-S, B-P, C-R, D-Q

B

A-S, B-Q, C-R, D-S

C

A-S, B-R, C-P, D-Q

D

A-Q, B-P, C-R, D-S

Question 176: Palette 176/192

Allen MCQ

Equal currents are flowing in two infinitely long separate wires lying along x and y-axes in the directions shown in figure. Match the following two columns.

Column-I	Column-II
(A) Magnetic field at (a, a) (B) Magnetic field at (-a. - a) (C) Magnetic field at (a, -a) (D) Magnetic field at (-a, a)	(P) along positive y-axis (Q) along positive z-axis (R) along negative z-axis (S) zero

A

A-P, B-Q, C-S, D-R

B

A-Q, B-R, C-S, D-S

C

A-R, B-S, C-P, D-R

D

A-S, B-P, C-Q, D-S

Question 177: Palette 177/192

Allen MCQ

Equal currents are flowing in four infinitely long wires. Distance between two wires is same and directions of currents are shown in figure. Match the following two columns.

Column-I	Column-II
(A) Force on wire-1 (B) Force on wire-2 (C) Force on wire-2 (D) Force on wire-4	(P) Inwards (Q) Leftwards (R) Rightwards (S) Zero

A

A-Q, B-R, C-Q, D-R

B

A-R, B-Q, C-P, D-R

C

A-Q, B-P, C-Q, D-P

D

A-P, B-R, C-P, D-R

Question 178: Palette 178/192

Allen MCQ

Three wires are carrying same constant current i in different directions. Four loops enclosing the wires in different manners are shown in figure. The direction of $d\vec{\ell}$ is shown in the figure.

Column-I	Column-II
(A) Along close Loop-1 (B) Along close Loop-2 (C) Along close Loop-3 (D) Along close Loop-4	(P) $\oint\vec{B}d\vec{\ell}=\mu_0i$ (Q) $\oint\vec{B}\cdot d\vec{\ell}=-\mu_0i$ (R) $\oint\vec{B}\cdot d\vec{\ell}=0$ (S) $\oint\vec{B}\cdot d\vec{\ell}=2\mu_0i$

A

A-Q, B-P, C-R, D-R

B

A-P, B-R, C-S, D-S

C

A-R, B-P, C-S, D-P

D

A-R, B-Q, C-Q, D-Q

Question 179: Palette 179/192

Allen Match the Columns

Side of cube is 'a' and wire AB, BC, CH and CE are insulated with each other. If each having current i, then match the following. External magnetic field applied along positive x-axis as $\vec{B}=B_{0}\hat{i}$ Column-I(Magnitude of force due to external magnetic field only) Column-II

Column-I	Column-II
(A) On AB (B) On BC (C) On CH (D) On CE	(P) Zero (Q) $\sqrt{2}iB_{0}a$ (R) $iB_{0}a$ (S) $2iB_{0}a$

A

A – R, B – P, C – R, D – Q

B

A – P, B – P, C – S, D – Q

C

A – Q, B – S, C – R, D – S

D

A – S, B – R, C – D, D – Q

Question 180: Palette 180/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Force on a current carrying wire of length $\overrightarrow{d\ell}$ placed in magnetic field $\vec{B}$ is given by $\overrightarrow{dF} = id\overrightarrow{\ell} \times \vec{B}$
Reason (R): Net force on a current carrying loop in a non-uniform magnetic field must be non-zero.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 181: Palette 181/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The ferromagnetic substances obey Curie's law.
Reason (R): At Curie point ferromagnetic substances start behaving as paramagnetic substances.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 182: Palette 182/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The surface integral of magnetic field over any closed surface is always zero.
Reason (R): Magnetic poles always exists in pair.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 183: Palette 183/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): A moving charge produces magnetic field.
Reason (B): A current element produces magnetic field.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 184: Palette 184/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Parallel wires carrying currents in same direction attracts each other due to magnetic force.
Reason (R) : Two electron beams moving parallel to each other repel each other due to electric force.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 185: Palette 185/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Ampere's circuital law is not suitable for a finite straight wire carrying current I.
Reason (R) : One cannot calculate magnetic field due to a finite straight current carrying wire by using Biot Savart Law.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 186: Palette 186/192

Allen MCQ

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The diamagnetic substances do not obey Curie's law.
Reason (R) : At Curie point ferromagnetic substances start behaving as paramagnetic substances.
In the light of the above statements,
choose the most appropriate answer from the options given below:

A

Both (A) and (R) are true and (R) is the correct explanation of (A).

B

Both (A) and (R) are true and (R) is NOT the correct explanation of (A).

C

(A) is true but (R) is false.

D

(A) is false but (R) is true.

Question 187: Palette 187/192

Allen MCQ

Statement-1: In an isolated conductor, free electrons keep on moving but no net magnetic force acts on a conductor in a magnetic field. Statement-2 : In a conductor, the average velocity of thermal motion of electrons is zero. Hence no current flows through the conductor.

A

If both statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1.

B

If both statements are TRUE but STATEMENT 2 is not the correct explanation of STATEMENT 1.

C

If STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.

D

If STATEMENT 1 is FALSE but STATEMENT 2 is TRUE.

Question 188: Palette 188/192

Allen MCQ

A particle with charge Q is moving in fields of combination given below. Match for the most correct possible path/s. Then match the following :-

Column-I	Column-II
(A) Uniform $\vec{E}$ (B) Uniform $\vec{B}$	(P) Straight line (Q) Parabola (R) Circular

A

A → PQ, B → PR

B

A → P, B → R

C

A → Q, B → PR

D

A → P, B → PQ

Question 189: Palette 189/192

Allen Match the Columns

Match the Column I with Column II -

Column-I	Column-II
(A) Paramagnetic substance (B) Diamagnetic substance (C) Super conductor (D) Ferromagnetic substance	(P) $\chi_{m} = -1$ (Q) $\chi_{m} < 0$ (R) $\chi_{m} >> 1$ (S) $\mu_{r} > 1$

A

A → S, B → Q, C → P, D → R

B

A → R, B → P, C → Q, D → S

C

A → S, B → P, C → Q, D → R

D

A → R, B → Q, C → P, D → S

Question 190: Palette 190/192

Allen MCQ

A magnetic field is applied at perpendicular to the axis of cylindrical discharge tube then cathode and positive rays deflected in –

A

Same direction.

B

Opposite direction.

C

Mutually perpendicular direction.

D

No deflection for both.

Question 191: Palette 191/192

Allen MCQ

A square current carrying loop of side 'a' produced magnetic field at its centre is 'B'. Find magnetic moment of this loop in terms of 'B'.

A

$\frac{\pi a^{3}B}{2\sqrt{2}\mu_{0}}$

B

$\frac{8\pi a^{3}B}{\mu_{0}}$

C

$\frac{\pi a^{2}B}{2\sqrt{2}\mu_{0}}$

D

$\frac{8\pi a^{2}B}{\mu_{0}}$

Question 192: Palette 192/192

Allen MCQ

Two long parallel wires carry i and 2i current in same direction. Magnetic field just between the wires is 'B'. If 2i current is switched off then magnetic field at the same point is :-

A

2B

B

B

C

B/2

D

$\sqrt{2}$ B