A proton moving with a velocity of $8 \times 10^5 \mathrm{~ms}^{-1}$ enters a uniform magnetic fleld normal to the direction of the magnetic field. If the radius of the circular path of the proton in the magnetic field is 8.3 cm , then the magnitude of the magnetic field is

(Charge of proton $=1.6 \times 10^{-19} \mathrm{C}$ and mass of the proton $=1.66 \times 10^{-27} \mathrm{~kg}$ )

The number of turns of two circular coils $A$ and $B$ are 300 and 200 respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1: 2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is

Two long straight parallel wires carry currents of 8 A and 10 A in opposite directions. If the distance of separation between the wires is 9 cm , then the net magnetic field at a point between the two wires, which is at a perpendicular distance of 4 cm from the wire carrying 8 A current is

An alpha particle moving with certain speed towards east enters a uniform magnetic field directed vertically up. The alpha particle will then move in

A solenoid of 1000 turns per metre has a core of material with relative permeability 400 . The windings of the solenoid are insulated from the core and a current of 2 A is passed through the solenoid. Then, the value of the magnetic intensity inside the solenoid is

The magnetic field due to a current carrying circular coil on its axis at a distance of $\sqrt{2} \mathrm{~d}$ from the centre of the coil is $B$. If $d$ is the diameter of the coil, then the magnetic field at the centre of the coil is

A square coil of side 10 cm having 200 turns is placed in a uniform magnetic field of 2 T such that the plane of the coil is in the direction of magnetic field. If the current through the coil is 3 mA , then the torque acting on the coil is

Two identical wires, carrying equal currents are bent into circular coils $A$ and $B$ with 2 and 3 turns respectively. The ratio of the magnetic fields at the centres of the coils $A$ and $B$ is

A current of 4 A is passed through a square loop of side 5 cm made of a uniform manganin wire as shown in the figure. The magnetic field at the centre of the loop is

A proton and an alpha particle moving with equal speeds enter normally into a uniform magnetic field. The ratio of times taken by the proton and the alpha particle to make one complete revolution in the magnetic field is

A solenoid of length 50 cm and radius 10 cm has two closely wound layers of windings 100 turns each. If a current of 2.5 A is passing through the windings, the magnetic field (in $10^{-4} \mathrm{~T}$ ) at a point 5 cm from the axis is

A square loop of side $a$ and carrying a current $I$ is suspended from an insulating hanger of a spring balance as shown in figure. The transverse magnetic field $B$ directed into the paper occurs only at the bottom side of the loop. When direction of current in the loop is reversed, the change in the reading of spring balance is

A current carrying loop is placed in a uniform magnetic field $B$ in different orientations I, II, III and IV as shown in the figure. The correct order of decreasing potential energy is

( $\hat{\mathbf{n}}=$ unit vector normal to the plane of the loop)

A current $i$ is flowing through a wire of length ' $L$ '. If it is made into a circular loop of one turn, then its magnetic moment is

It is found that a non-zero current element is unable to produce any magnetic field at a particular point. Then the angle between the current element and the position vector of that point with respect to the current element is

Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire $C$ be $\mathbf{F}$. If the wire $B$ is oved without disturbing the other two wires, then the force per unit length on wire $A$ is

A current $i$ flows in an infinitely long, straight and thin walled pipe, then

A closely wound solenoid of 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 cm . If the current carried is 8 A , then the magnitude of the magnetic field inside the solenoid near its centre is approximately

A charge $q$ moves with a velocity $2 \mathrm{~ms}^{-1}$ along $X$-axis in a uniform magnetic field $\mathbf{B}=(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ T, then charge will experience a force

The magnetic field at a perpendicular distance of one metre from a wire carrying current of 1 A is

A circular coil of area $2 \mathrm{~cm}^2$ has 1000 turns. If the current through the coil is 1 A , then its magnetic moment is

Two infinitely long thin wires are placed at $(1 \mathrm{~cm}, 0 \mathrm{~cm})$ and $(2 \mathrm{~cm}, 0 \mathrm{~cm})$ as shown in the figure.

The same current $i$ flows in both the wires in the same direction, say, into the page. Let the magnetic field at the origin due to these wires is $\mathbf{B}$. If $B_0$ is the magnitude of the magnetic field, if only the wire at $(1 \mathrm{~cm}, 0 \mathrm{~cm})$ was present, then the value of $\frac{B}{B_0}$ is

A toroid core has inner radius of 0.24 m and outer radius of 0.26 m . A current of 10 A flows through the wire having 2500 turns around it. Find the magnetic field inside the core of the toroid

A current carrying loop $A B C D$ has two circular arcs $A D$ and $B C$ with radius 1 cm and 2 cm respectively, as shown in the figure. The two arcs $A D$ and $B C$ subtend a common angle $30^{\circ}$ at the centre $O$. If the current flowing in the loop is $\frac{12}{\pi} \mathrm{~A}$. Then, the magnitude of net magnetic field at $O$ is (given, $\mu_0=4 \pi \times 10^{-7}$ )

Three parallel wires $a, b$ and $c$ carrying currents $i_a, i_b$ and $i_c$ as shown in the figure are placed next to each other.

The magnitude force on a length $l$ of the wire $a$, if $d_2=2 d_1, i_b=i_a$ and $i_c=4 i_a$ is

Statement I A uniform electric field and a uniform magnetic field are pointed in the same direction. If an electron is projected in the same direction, the electron velocity will decrease in magnitude.

Statement II Two infinite long parallel wires are carrying current in the same direction. The magnetic field at a point mid-way between the wires is zero.

Statement III No net force acts on a rectangular coil carrying a steady current, when suspended in a uniform magnetic field.

Which of the following is correct?

Two parallel conductor each 50 m long, separated by 0.2 m experience a force of 1 N . If the current in first conductor is twice that of the second conductor, then what is the current in the second conductor?

$ \left(\mu=4 \pi \times 10^{-7}\right) $

A long solenoid with 10.0 turn $/ \mathrm{cm}$ and a radius of 8 cm carries a current of 7 mA . A current carrying straight conductor is located along the central axis of the solenoid. If the direction of resulting magnetic field is $60^{\circ}$ to axial direction at a point 5 cm from the axis of the solenoid along the radial direction, then the current in the conductor is [take, $\sqrt{2}=1.4, \sqrt{3}=1.7$ ]

A horizontal wire carries 160 A current below which another wire of linear density $10 \mathrm{~g} / \mathrm{m}$ carrying a current is kept at 4 cm distance. If the wire kept below hangs in air, what is the current in this wire, when the direction of current in both the wires is same? $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right.$ and $\left.\mu_0=4 \pi \times 10^{-7}\right)$

A long solenoid has 70 turns / cm and carries current $I$. An electron moves within the solenoid in a circle of radius 2.5 cm perpendicular to the solenoid axis. If the speed of the electron is $4.4 \times 10^6 \mathrm{~m} / \mathrm{s}$, then the current $I$ in the solenoid is

(take $\mu_0=4 \pi \times 10^{-7}$ Si unit, mass electron $=9 \times 10^{-31}$

kg , charge of electron $1.6 \times 10^{-19} \mathrm{C}$ )

A current $I=5 \mathrm{~A}$ flows along a thin wire shaped as shown in figure. The radius of curved part of the wire is equal to $R=100 \mathrm{~mm}$, the angle $2 \phi=90^{\circ}$. The magnitude of magnetic field at the point $O$ is approximately

$ \left(\text { use, } \frac{\mu_0}{4 \pi}=10^{-7} \mathrm{~T} \mathrm{~mA}^{-1}\right) $

A toroid has a core (non-ferro magnetic) of inner radius 24 cm and outer radius 26 cm around which 2000 turns of a wire is wound. If the current in the wire is 12 A , the magnetic field inside the core of the toroid is

A straight wire of mass 0.2 kg and length 1.5 m carries a current 2A is shown in the figure. It is suspended in mid-air by a uniform magnetic field $B$ pointing to the plane of paper. The magnitude of magnetic field is (ignore, earth's magnetic field and assume $g=10 \mathrm{~m} / \mathrm{s}^2$ )

The ratio of the magnetic field inside a solenoid at an axial point well inside and at an axial end point is

An infinite long wire lying along the $Y$-axis, is carrying a current $I$ as shown in the figure. The magnetic flux through a circular loop of radius $R$ in the $x y$-plane is [assume, $\mu_0=$ magnetic in free space permeability]

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. A point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

A solenoid of length 2 m carries a current of 20 A . The diameter of the solenoid is 3 cm . If the magnetic field inside the solenoid is 20 mT , then the length of wire forming the solenoid is (assume, $\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}$ )

Two tangent galvanometers $A$ and $B$ have coils of radii 8 cm and 16 cm respectively and having resistance of 8 $\Omega$ each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30^{\circ}$ and $60^{\circ}$, respectively. If $A$ has 2 turns, then $B$ must have

A particle of charge $q$ and mass $m$ moves in a circular orbit of radius $r$ with angular speed $\omega$. The ratio of the magnitude of its magnetic moment to that of its angular momentum is

A circular coil of 10 turns and radius 10 cm is placed in a uniform magnetic field of 0.1 T normal to the plane of the coil. If the current in the coil is 5 A , then the magnitude of the torque on the coil is

A 50 cm long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?