Current Carrying Loop in External Magnetic Field

A rectangular coil PQ has $2n$ turns, an area $2a$ and carries a current $2I$, (refer figure). The plane of the coil is at $60^{\text{o}}$ to a horizontal uniform magnetic field of flux density $B$. The torque on the coil due to magnetic force is

A conducting ring of mass $2 \mathrm{kg}$ and radius $0.5 \mathrm{m}$ is placed on a smooth horizontal plane. The ring carries a current $i=4 \mathrm{A}$. A horizontal magnetic field $B=10 \mathrm{T}$ is switched on at time $t=0$ as shown in the figure. The initial angular acceleration of the ring will be

A cone made of insulating material has a total charge $\mathit{Q}$ spread uniformly over its sloping surface having a slant length $\mathit{L}$. The energy required to take a test charge $\mathit{q}$ from infinity to apex $\mathrm{A}$ of the cone will be
 

A wire loop carrying current $i$ is placed in the $x-y$ plane as shown in the figure. If an external uniform magnetic field $\overrightarrow{B}=B\hat{\text{i}}$ is switched on, then the torque acting on the loop is

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3} \mathrm{J}$ of work to turn it through $60°$. The torque needed to maintain the needle in this position will be

Which of the following is the correct orientation of unstable equilibrium.

When a current carrying loop is placed in a uniform magnetic field with its magnetic moment directed anti-parallel to the field then equilibrium is

Torques ${\tau }_1$ and ${\tau }_2$ are required for a magnetic needle to remain perpendicular to the magnetic fields $B_1$ and $B_2$ at two different places. The ratio $B_1:B_2$ is

A magnet of magnetic moment $2 \mathrm{J} {\mathrm{T}}^{-1}$ is aligned in the direction of magnetic field of $0.1\mathrm{T}.$
What is the net work done to bring the magnet normal to the magnetic field?

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 ${60}^{\mathrm{o}}$ is $W$. Now, the torque required to keep the magnet in this new position is

A rectangular loop of sides $10 \mathrm{cm}$ and $5 \mathrm{cm}$, carrying a current $I$ of $12 \mathrm{A}$, is placed in different orientations as shown in the figure below.
(a)  (b)

(c)  (d)

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive $z-$direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium?

A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

A beam of neutrons performs circular motion of radius, $r=1 m,$ under the influence of an inhomogeneous magnetic field with inhomogeneity extending over $\Delta r=0.01 m.$ The speed of the neutrons is $54 {\mathrm{ms}}^{-1}.$ The mass and magnetic moment of the neutrons respectively are $1.67\times {10}^{-27} \mathrm{kg}$ and $9.67\times {10}^{-27} \mathrm{J}/T.$ The average variation of the magnetic field over $\Delta r$ is approximately.

A magnet of magnetic moment $M$ is situated with its axis along the direction of a magnetic field of strength $B$. The work done in rotating it by an angle of $180°$ will be

A wire of length $L$ is bent in the form of a circular coil and current $i$ is passed through it. If this coil is placed in a magnetic field, then the torque acting on the coil will be maximum when the number of turns is

A coil in the shape of an equilateral triangle of side $0.02 \mathrm{m}$ is suspended from its vertex, such that it is hanging in a vertical plane between the pole pieces of permanent magnet producing a uniform field of $5\times {10}^{-2} \mathrm{T}.$ If a current of $0.1 \mathrm{A}$ is passed through the coil, what is the couple acting?

A magnet of magnetic moment $50\hat{\mathrm{i}} \mathrm{A} {\mathrm{m}}^2$ is placed along the $X$-axis in a magnetic field $\overrightarrow{\mathrm{B}}=\left(0.5\hat{\mathrm{i}}+3.0\hat{\mathrm{j}}\right) \mathrm{T}$. The torque acting on the magnet is :-

A current carrying loop is free to turn in a uniform magnetic field. The loop will then come into equilibrium when its plane is inclined at

Four wires, of equal length, are bent in the form of four loops, $P, Q, R$ and $S$. They are suspended in a uniform magnetic field and same current is passed through them. The maximum torque will act on

A circular loop with $N$ turns has radius $r$. It lies in x-y plane carrying current $I$ in anti-clockwise direction. If the magnetic field in the region is $\overrightarrow{B}=B_0\widehat{i},$ then find the torque $\left(\overrightarrow{\tau }\right)$ acting on the loop.