Torque on Current Loop, Magnetic Dipole

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

$Q$ charge is uniformly distributed over the curve surface of a right circular cone of semi-vertical angle $\theta$ and height $h$. The cone is uniformly rotated about its axis at angular velocity $\omega$. Calculate associated magnetic dipole moment. $(h>R)$

The magnetic moment of the current carrying loop shown in the figure is equal to

A steel wire of length $l$ and magnetic moment $M$ is bent into a semicircular arc of radius $R$. The new magnetic moment is

A bar magnet suspended by a horse hair lies in the magnetic meridian when there is no twist in the hair, On turning the upper end of the hair through $150°$ from the meridian the magnet is deflected through $30°$ form the meridian. Then the angle through which the upper end of the hair has to be twisted to deflect the magnet through $90°$ from the meridian is ,

A uniform rigid ring of radius $r$ and unknown mass is placed on a non-conducting horizontal table-top where exists a uniform horizontal magnetic field of Induction $B$ as shown in figure. Now a current $I$ that is double that of minimum current required to flip over the ring is switched on in the coil.

A bar magnet of length $10 \mathrm{cm}$ and pole strength $20 \mathrm{A}-\mathrm{m}$ is deflected through $30°$ from the magnetic meridian. If earth's horizontal component field is $\frac{320}{4\pi }\mathrm{A} {\mathrm{m}}^{-1}$. The moment of the deflecting couple is

A square loop of side $l$ is kept in a uniform magnetic field $B$ such that its plane makes an angle with $\overrightarrow{B}$. The loop carries a current $i$. The torque experienced by the loop in this position is

A rectangular loop consists of $N$ closed wrapped turns and has dimensions $a\times b$. The loop is hinged along the Y-axis. What is the magnitude of the torque exerted on the loop by a uniform magnetic field $B=B_0$ direction shown. The torque acting on the loop is

A nonconducting sphere has mass $8.0\mathrm{kg}$ and radius $0.2 \mathrm{m}$. A flat compact coil of wire with $50$ turns is wrapped tightly around it, with each turn concentric with the sphere. As shown in the figure, the sphere is placed on an inclined plane that slopes downward to the left, making an angle $\theta$ with the horizontal, so that the coil is parallel to the inclined plane. A uniform magnetic field of $0.35 \mathrm{T}$ vertically upward exists in the region of the sphere. If the sphere rests in equilibrium on the inclined plane, the current through the coil is closest to

The rectangular loop of dimensions $0.4 \mathrm{m}\times 0.2 \mathrm{m}$ shown in the figure consists of $50$ closely wrapped turns and is hinged along the $z$-axis. The plane of the loop makes an angle of $30°$ with the $y$-axis. The current in the windings is $0.5 \mathrm{A}$.

The torque exerted on the loop in this position by a magnetic field $\overrightarrow{B}=\hat{j}1.0 \mathrm{T}$

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

A compass needle just above a wire in which electrons are moving towards east, will point

Find the torque in a conductor having current $2\mathrm{A}$, flux density $50 \mathrm{units}$, length $15 \mathrm{cm}$ and distance of $8 \mathrm{cm}$.

What is value of bohr magneton?

In Bohr's hydrogen like atom magnetic dipole moment in ${\mathrm{n}}^{\mathrm{th}}$ orbit is expressed as.