Current Carrying Loop in External Magnetic Field

The figure shows a  current-carrying square loop $ABCD$ of side $10 \mathrm{cm}$ and current $i=10 \mathrm{A}$. The magnetic moment $\overrightarrow{M}$ of the loop is

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

The magnetic needle of a vibration magnetometer makes 12 oscillations per minute in the horizontal component of earth's magnetic field. When an external short bar magnet is placed at some distance along the axis of the needle in the same line, it makes 15 oscillations per minute. If the poles of the bar magnet are interchanged, the number of oscillations it makes per minute is $\sqrt{n}$. What is the value of $n$?

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)

Two magnets held together in earth's magnetic field when the same polarity together causes $12 \text{v}\text{i}\text{b}/\min$ and when opposite poles $4 \text{v}\text{i}\text{b}/\text{m}\text{i}\text{n}$. If the ratio of magnetic moments is $\frac{x}{8}$, what is the value of $x$?

Calculate the couple (in $\mu \mathrm{N} \mathrm{m}$) acting on a magnet of length $10 \mathrm{cm}$ and pole strength $15 \mathrm{A} \mathrm{m}$, kept in a field of $B=2\times {10}^{-5} \mathrm{T}$ at an angle of $30°$.

A compass needle is free to rotate in a horizontal plane. Its magnetic moment is $60 \mathrm{A} {\mathrm{m}}^2.$ When it is pointing geographical north, it experiences a torque of $1.2\times {10}^{-3} \mathrm{N} \mathrm{m}$ due to earth's magnetic field. If earth's magnetic field in horizontal direction is $40\times {10}^{-6} \mathrm{T},$ the declination (in degree) at that place is?

A square coil of edge $l$ having $n$ turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is $m$. The minimum value of $B$ for which the coil will start tipping over is $\frac{1}{k}$, what is the value of $k$? Given that $mg=nil$ (All physical quantities are in SI unit)

A current carrying uniform square frame is suspended from hinged supports as shown in the figure such that it can freely rotate about its upper side. The length and mass of each side of the frame is $2 \mathrm{m}$ and $4 \mathrm{kg}$ respectively. A uniform magnetic field $\overrightarrow{\mathrm{B}}=(3\hat{\mathrm{i}}+4\hat{\mathrm{j}})$ is applied. When the wire frame is rotated to $45°$ from vertical and released it remains in equilibrium. If the magnitude of current (in A) in the wire frame is I then find $\left(\frac{3}{5}\right)$ $I .$

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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