Moving Charges and Magnetism — Class 12 Physics PYQs

A 1 cm segment of a wire lying along x-axis carries current of 0.5 A along +x direction. A magnetic field $\vec{B}=(0.4mT)\hat{j}+(0.6mT)\hat{k}$ is switched on, in the region. The force acting on the segment is
(A) $(2\hat{j}+3\hat{k})$ mN
(B) $(-3\hat{j}+2\hat{k})$ $\mu$N
(C) $(6\hat{j}+4\hat{k})$ mN
(D) $(-4\hat{j}+6\hat{k})$ $\mu$N

The magnetic field due to a small magnetic dipole of dipole moment 'M' at a distance 'r' from the centre along the axis of the dipole is given by
(A) $\frac{{\mu }_0}{4\pi }\times \frac{2M}{r^3}$
(B) $\frac{{\mu }_0}{4\pi }\times \frac{M}{r^3}$
(C) $\frac{{\mu }_0}{4\pi }\times \frac{M}{2r^3}$
(D) $\frac{{\mu }_0}{4\pi }\times \frac{2M}{r^2}$

A 1 cm straight segment of a conductor carrying 1 A current in x direction lies symmetrically at origin of Cartesian coordinate system. The magnetic field due to this segment at point (1m, 1m, 0) is
(A) $1.0\times 10^{-9}\hat{k}$ T
(B) $-1.0\times 10^{-9}\hat{k}$ T
(C) $\frac{5.0}{\sqrt{2}}\times 10^{-10}\hat{k}$ T
(D) $-\frac{5.0}{\sqrt{2}}\times 10^{-10}\hat{k}$ T

Assertion (A) : The deflection in a galvanometer is directly proportional to the current passing through it.
Reason (R) : The coil of a galvanometer is suspended in a uniform radial magnetic field.

Using Biot-Savart law, derive expression for the magnetic field ($\vec{B}$) due to a circular current carrying loop at a point on its axis and hence at its centre.

Define magnetic moment of a current-carrying coil. Write its SI unit.
(b) A coil of 60 turns and area $1.5\times 10^{-3}{m}^2$ carrying 2A current lies in a vertical plane. It experiences a torque of 0.12 Nm when placed in a uniform horizontal magnetic field. The torque acting on the coil changes to 0.05 Nm after the coil is rotated about its diameter by $90^{\circ }$. in the magnetic field. Find the magnitude of the magnetic field.

A proton moving with velocity $\vec{V}$ in a non-uniform magnetic field traces a path as shown in the figure.
The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points P, Q and R ? What can you say about relative magnitude of magnetic fields at these points ?
(ii) A current carrying circular loop of area A produces a magnetic field B at its centre. Show that the magnetic moment of the loop is $\frac{2BA}{{\mu }_0}\sqrt{\frac{A}{\pi }}$.
OR
(b) (i) Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.
(ii) A charged particle is moving in a circular path with velocity $\vec{V}$ in a uniform magnetic field B. It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will (1) the radius of its path (2) its time period of revolution change ?

A wire of length 4.4 m is bent round in the shape of a circular loop and carries a current of 1.0 A. The magnetic moment of the loop will be :
(A) 0.7 Am${}^2$
(B) 1.54 Am${}^2$
(C) 2.10 Am${}^2$
(D) 3.5 Am${}^2$

A loop carrying a current I clockwise is placed in x – y plane, in a uniform magnetic field directed along z-axis. The tendency of the loop will be to :
(A) move along x-axis
(B) move along y-axis
(C) shrink
(D) expand

Two charged particles, P and Q, each having charge q but of masses m${}_1$ and m${}_2$, are accelerated through the same potential difference V. They enter a region of magnetic field $\vec{B}(\perp \vec{v})$ and describe the circular paths of radii a and b respectively. Then $\sqrt{\frac{m_1}{m_2}}$ is equal to :
(A) a/b
(B) b/a
(C) a${}^2$/b${}^2$
(D) b${}^2$/a${}^2$