Magnetic Effect of Current
240 Questions
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Evening Slot
A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 $ \times $ 10-2 m. The magnetic field at the center of the triangle will be :
A.
2 $ \times $ 10-5 Wb/m2
B.
Zero
C.
8 $ \times $ 10-5 Wb/m2
D.
4 $ \times $ 10-5 Wb/m2
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
A Helmholtz coil has a pair of loops, each with $N$ turns and radius $R$. They are placed coaxially at distance $R$ and the same current ${\rm I}$ flows through the loops in the same direction. $P,$ midway between the centers $A$ and $C$, is given by [Refer to figure given below] :
A.
${{8N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}$
B.
${{8N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}$
C.
${{4N{\mu _0}{\rm I}} \over {{5^{1/2}}R}}$
D.
${{4N{\mu _0}{\rm I}} \over {{5^{3/2}}R}}$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 9th April Morning Slot
A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is :
A.
away from the wire
B.
towards the wire
C.
parallel to the wire along the current
D.
parallel to the wire opposite to the current
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 8th April Morning Slot
In a certain region static electric and magnetic fields exist. The magnetic field is given by $\overrightarrow B = {B_0}\left( {\widehat i + 2\widehat j - 4\widehat k} \right)$ . If a test charge moving with a velocity $\overrightarrow \upsilon = {\upsilon _0}\left( {3\widehat i - \widehat j + 2\widehat k} \right)$ experiences no force in that region, then the electric field in the region, in SI units, is :
A.
$\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {3\widehat i - 2\widehat j - 4\widehat k} \right)$
B.
$\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {\widehat i + \widehat j + 7\widehat k} \right)$
C.
$\overrightarrow E = {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$
D.
$\overrightarrow E = - {\upsilon _0}\,{B_0}\left( {14\widehat j + 7\widehat k} \right)$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 8th April Morning Slot
A magnetic dipole in a constant magnetic field has :
A.
maximum potential energy when the torque is maximum.
B.
zero potential energy when the torque is minimum.
C.
zero potential energy when the torque is maximum.
D.
minimum potential energy when the torque is maximum.
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of 75o. One of the fields has a magnitude of 15 mT. The dipole attains stable equilibrium at an angle of 30o with this field. The magnitude of the other field (in mT ) is close to
A.
11
B.
36
C.
1
D.
1060
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle $\theta $. If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :
A.
2S (R + G) = RG
B.
S (R + G) = RG
C.
2S = G
D.
2G = S
2016
JEE Mains
MCQ
JEE Main 2016 (Offline)
Two identical wires $A$ and $B,$ each of length $'l'$, carry the same current $I$. Wire $A$ is bent into a circle of radius $R$ and wire $B$ is bent to form a square of side $'a'$. If ${B_A}$ and ${B_B}$ are the values of magnetic fields at the centres of the circle and square respectively, then the ratio ${{{B_A}} \over {{B_B}}}$ is:
A.
${{{\pi ^2}} \over {16}}$
B.
${{{\pi ^2}} \over {8\sqrt 2 }}$
C.
${{{\pi ^2}} \over {8}}$
D.
${{{\pi ^2}} \over {16\sqrt 2 }}$
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
Two long current carrying thin wires, both with current $I,$ are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $'\theta '$ with the vertical. If wires have mass $\lambda $ per unit-length then the value of $I$ is :
($g=$ $gravitational$ $acceleration$ )
($g=$ $gravitational$ $acceleration$ )
A.
$2\sqrt {{{\pi gL} \over {{\mu _0}}}\tan \theta } $
B.
$\sqrt {{{\pi \lambda gL} \over {{\mu _0}}}\tan \theta } $
C.
$\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}} $
D.
$2\sin \theta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos \theta }}} $
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
A rectangular loop of sides $10$ $cm$ and $5$ $cm$ carrying a current $1$ of $12A$ is placed in different orientations as shown in the figures below :
If there is a uniform magnetic field of $0.3$ $T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium ?
A.
$(B)$ and $(D)$, respectively
B.
$(B)$ and $(C)$, respectively
C.
$(A)$ and $(B)$, respectively
D.
$(A)$ and $(C)$, respectively
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
A conductor lies along the $z$-axis at $ - 1.5 \le z < 1.5\,m$ and carries a fixed current of $10.0$ $A$ in $ - {\widehat a_z}$ direction (see figure). For a field $\overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T,$ find the power required to move the conductor at constant speed to $x=2.0$ $m$, $y=0$ $m$ in $5 \times {10^{ - 3}}s.$ Assume parallel motion along the $x$-axis.
A.
$1.57W$
B.
$2.97W$
C.
$14.85$ $W$
D.
$29.7W$
2012
JEE Mains
MCQ
AIEEE 2012
A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R.$ The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity $\omega .$ As a result of this rotation a magnetic field of induction $B$ is obtained at the center of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and very the radius of the disc then the variation of the magnetic induction at the center of the disc will be represented by the figure :
A.
B.
C.
D.
2012
JEE Mains
MCQ
AIEEE 2012
Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, denuteron and alpha particle are respectively ${r_p},{r_d}$ and ${r_\alpha }$. Which one of the following relation is correct?
A.
${r_\alpha } = {r_p} = {r_d}$
B.
${r_\alpha } = {r_p} < {r_d}$
C.
${r_\alpha } > {r_d} > {r_p}$
D.
${r_\alpha } = {r_d} > {r_p}$
2011
JEE Mains
MCQ
AIEEE 2011
A current $I$ flows in an infinitely long wire with cross section in the form of a semi-circular ring of radius $R.$ The magnitude of the magnetic induction along its axis is:
A.
${{{\mu _0}I} \over {2{\pi ^2}R}}$
B.
${{{\mu _0}I} \over {2\pi R}}$
C.
${{{\mu _0}I} \over {4\pi R}}$
D.
${{{\mu _0}I} \over {{\pi ^2}R}}$
2010
JEE Mains
MCQ
AIEEE 2010
Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by
A.
B.
C.
D.
2009
JEE Mains
MCQ
AIEEE 2009
A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $=a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is ${30^ \circ }.$ Another straight thin wire steady current ${I_1}$ flowing out of the plane of the paper is kept at the origin.
Due to the presence of the current ${I_1}$ at the origin:
A.
The forces on $AD$ are $BC$ are zero.
B.
The magnitude of the net force on the loop is given by ${{{I_1}I} \over {4\pi }}{\mu _0}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{$\scriptstyle \pi $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 3$}}\left( {a + b} \right)} \right].$
C.
The magnitude of the net force on the loop is given by ${{{\mu _0}I{I_1}} \over {24ab}}\left( {b - a} \right).$
D.
The forces on $AB$ and $DC$ are zero.
2009
JEE Mains
MCQ
AIEEE 2009
A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $=a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is ${30^ \circ }.$ Another straight thin wire steady current ${I_1}$ flowing out of the plane of the paper is kept at the origin.
The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is :
A.
${{{\mu _0}I\left( {b - a} \right)} \over {24ab}}$
B.
${{{\mu _0}I} \over {4\pi }}\left[ {{{b - a} \over {ab}}} \right]$
C.
${{{\mu _0}I} \over {4\pi }}\left[ {2\left( {b - a} \right) + {\raise0.5ex\hbox{$\scriptstyle \pi $}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 3$}}\left( {a + b} \right)} \right]$
D.
zero
2008
JEE Mains
MCQ
AIEEE 2008
A horizontal overhead powerline is at height of $4m$ from the ground and carries a current of $100A$ from east to west. The magnetic field directly below it on the ground is
$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)$
$\left( {{\mu _0} = 4\pi \times {{10}^{ - 7}}\,\,Tm\,\,{A^{ - 1}}} \right)$
A.
$2.5 \times {10^{ - 7}}\,T$ southward
B.
$5 \times {10^{ - 6}}\,T$ northward
C.
$5 \times {10^{ - 6}}\,T$ southward
D.
$2.5 \times {10^{ - 7}}\,T$ northward
2007
JEE Mains
MCQ
AIEEE 2007
A charged particle with charge $q$ enters a region of constant, uniform and mutually orthogonal fields $\overrightarrow E $ and $\overrightarrow B $ with a velocity $\overrightarrow v $ perpendicular to both $\overrightarrow E $ and $\overrightarrow B, $ and comes out without any change in magnitude or direction of $\overrightarrow v $. Then
A.
$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{E^2}$
B.
$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{B^2}$
C.
$\overrightarrow v = \overrightarrow B \times \overrightarrow E /{B^2}$
D.
$\overrightarrow v = \overrightarrow E \times \overrightarrow B /{E^2}$
2007
JEE Mains
MCQ
AIEEE 2007
Two identical conducting wires $AOB$ and $COD$ are placed at right angles to each other. The wire $AOB$ carries an electric current ${I_1}$ and $COD$ carries a current ${I_2}$. The magnetic field on a point lying at a distance $d$ from $O$, in a direction perpendicular to the plane of the wires $AOB$ and $COD$ , will be given by
A.
${{{\mu _0}} \over {2\pi d}}\left( {I_1^2 + I_2^2} \right)$
B.
${{{\mu _0}} \over {2\pi }}{\left( {{{{I_1} + {I_2}} \over d}} \right)^{{1 \over 2}}}$
C.
${{{\mu _0}} \over {2\pi d}}{\left( {I_1^2 + I_2^2} \right)^{{1 \over 2}}}$
D.
${{{\mu _0}} \over {2\pi d}}\left( {{I_1} + {I_2}} \right)$
2007
JEE Mains
MCQ
AIEEE 2007
A charged particle moves through a magnetic field perpendicular to its direction. Then
A.
Kinetic energy changes but the momentum is constant
B.
the momentum changes but the kinetic energy is constant
C.
both momentum and kinetic energy of the particle are not constant
D.
both momentum and kinetic energy of the particle are constant
2007
JEE Mains
MCQ
AIEEE 2007
A long straight wire of radius $a$ carries a steady current $i.$ The current is uniformly distributed across its cross section. The ratio of the magnetic field at $a/2$ and $2a$ is
A.
$1/2$
B.
$1/4$
C.
$4$
D.
$1$
2007
JEE Mains
MCQ
AIEEE 2007
A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then
A.
the magnetic field at all points inside the pipe is the same, but not zero
B.
the magnetic field is zero only on the axis of the pipe
C.
the magnetic field is different at different points inside the pipe
D.
the magnetic field at any point inside the pipe is zero
2006
JEE Mains
MCQ
AIEEE 2006
In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a
A.
helix
B.
straight line
C.
ellipse
D.
circle
2006
JEE Mains
MCQ
AIEEE 2006
A long solenoid has $200$ turns per $cm$ and carries a current $i.$ The magnetic field at its center is $6.28 \times {10^{ - 2}}\,\,\,Weber/{m^2}.$ Another long solenoid has $100$ turns per $cm$ and it carries a current ${i \over 3}$. The value of the magnetic field at its center is
A.
$1.05 \times {10^{ - 2}}\,\,Weber/{m^2}$
B.
$1.05 \times {10^{ - 5}}\,\,Weber/{m^2}$
C.
$1.05 \times {10^{ - 3}}\,\,Weber/{m^2}$
D.
$1.05 \times {10^{ - 4}}\,\,Weber/{m^2}$
2005
JEE Mains
MCQ
AIEEE 2005
A charged particle of mass $m$ and charge $q$ travels on a circular path of radius $r$ that is perpendicular to a magnetic field $B.$ The time taken by the particle to complete one revolution is
A.
${{2\pi {q^2}B} \over m}$
B.
${{2\pi mq} \over B}$
C.
${{2\pi m} \over {qB}}$
D.
${{2\pi qB} \over m}$
2005
JEE Mains
MCQ
AIEEE 2005
A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then
A.
its velocity will increase
B.
Its velocity will decrease
C.
it will turn towards left of a direction of motion
D.
it will turn towards right of direction of motion
2005
JEE Mains
MCQ
AIEEE 2005
Two thin, long, parallel wires, separated by a distance $'d'$ carry a current of $'i'$ $A$ in the same direction. They will
A.
repel each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
B.
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi d} \right)$
C.
repel each other with a force $_0{i^2}/\left( {2\pi {d^2}} \right)$
D.
attract each other with a force of ${\mu _0}{i^2}/\left( {2\pi {d^2}} \right)$
2005
JEE Mains
MCQ
AIEEE 2005
Two concentric coils each of radius equal to $2$ $\pi $ $cm$ are placed at right angles to each other. $3$ ampere and $4$ ampere are the currents flowing in each coil respectively . The magnetic induction in Weber / ${m^2}$ at the center of the coils will be
$\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)$
$\left( {\mu = 4\pi \times {{10}^{ - 7}}Wb/A.m} \right)$
A.
${10^{ - 5}}$
B.
$12 \times {10^{ - 5}}$
C.
$7 \times {10^{ - 5}}$
D.
$5 \times {10^{ - 5}}$
2004
JEE Mains
MCQ
AIEEE 2004
The magnetic field due to a current carrying circular loop of radius $3$ $cm$ at a point on the axis at a distance of $4$ $cm$ from the centre is $54\,\mu T.$ What will be its value at the center of loop?
A.
$125\,\mu T$
B.
$150\,\mu T$
C.
$250\,\mu T$
D.
$75\,\mu T$
2004
JEE Mains
MCQ
AIEEE 2004
A long wire carries a steady current. It is bent into a circle of one turn and the magnetic field at the centre of the coil is $B.$ It is then bent into a circular loop of $n$ turns. The magnetic field at the center of the coil will be
A.
$2n$ $B$
B.
${n^2}\,B$
C.
$nB$
D.
$2{n^2}\,B$
2004
JEE Mains
MCQ
AIEEE 2004
Two long conductors, separated by a distance $d$ carry current ${I_1}$ and ${I_2}$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is
A.
$ - {{2F} \over 3}$
B.
${F \over 3}$
C.
$-2F$
D.
$ - {F \over 3}$
2004
JEE Mains
MCQ
AIEEE 2004
A current $i$ ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is
A.
${{{\mu _0}} \over {4\pi }},{{2i} \over r}$ tesla
B.
zero
C.
infinite
D.
${{2i} \over r}$ tesla
2003
JEE Mains
MCQ
AIEEE 2003
A particle of charge $ - 16 \times {10^{ - 18}}$ coulomb moving with velocity $10m{s^{ - 1}}$ along the $x$-axis enters a region where a magnetic field of induction $B$ is along the $y$-axis, and an electric field of magnitude ${10^4}V/m$ is along the negative $z$-axis. If the charged particle continues moving along the $x$-axis, the magnitude of $B$ is
A.
${10^3}Wb/{m^2}$
B.
${10^5}Wb/{m^2}$
C.
${10^{16}}Wb/{m^2}$
D.
${10^{ - 3}}Wb/{m^2}$
2003
JEE Mains
MCQ
AIEEE 2003
A particle of mass $M$ and charge $Q$ moving with velocity $\overrightarrow v $ describe a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B.$ The network done by the field when the particle completes one full circle is
A.
$\left( {{{M{v^2}} \over R}} \right)2\pi R$
B.
zero
C.
$B\,\,Q\,2\pi R$
D.
$B\,Qv\,2\pi R$
2002
JEE Mains
MCQ
AIEEE 2002
If a current is passed through a spring then the spring will
A.
expand
B.
compress
C.
remains same
D.
none of these
2002
JEE Mains
MCQ
AIEEE 2002
Wires $1$ and $2$ carrying currents $i{}_1$ and $i{}_2$ respectively are inclined at an angle $\theta $ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?
A.
${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\tan \,\theta $
B.
${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta $
C.
${{{\mu _0}} \over {2\pi r}}{i_1}{i_2}\,dl\,\cos \,\theta $
D.
${{{\mu _0}} \over {4\pi r}}{i_1}{i_2}\,dl\,\sin \,\theta $
2002
JEE Mains
MCQ
AIEEE 2002
If an electron and a proton having same momentum enter perpendicular to a magnetic field, then
A.
curved path of electron and proton will be same (ignoring the sense of revolution)
B.
they will move undeflected
C.
curved path of electron is more curved than that of the proton
D.
path of proton is more curved.
2002
JEE Mains
MCQ
AIEEE 2002
If in a circular coil $A$ of radius $R,$ current $I$ is flowing and in another coil $B$ of radius $2R$ a current $2I$ is flowing, then the ratio of the magnetic fields ${B_A}$ and ${B_B}$, produced by them will be
A.
$1$
B.
$2$
C.
$1/2$
D.
$4$
2002
JEE Mains
MCQ
AIEEE 2002
The time period of a charged particle undergoing a circular motion in a uniform magnetic field is independent of its
A.
speed
B.
mass
C.
charge
D.
magnetic induction