Current Carrying Loop in External Magnetic Field

Two insulated rings, one of slightly smaller diameter than the other, are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady current is set up in each of them.

A thin non-conducting disc of radius $R$ is rotating clockwise (see figure) with an angular velocity $\omega$ about its central axis, which is perpendicular to its plane. Both its surface carry $+\mathrm{ve}$ charges of uniform surface density. Half the disc is in region of a uniform, unidirectional magnetic field $B$ parallel to the disc, as shown. Then,

In the figure shown a coil of single turn is would on a sphere of radius $R$ and mass $m$. The plane of the coil is parallel to the plane and lies in the equatorial plane of the sphere. Current in the coil is $i$. The value of $B$ if the sphere is in equilibrium is

A square current carrying loop made of thin wire and having a mass $m=10 \mathrm{g}$ can rotate without friction with respect to the vertical axis $O{O}_1$, passing through the centre of the loop at the right angles to two opposite sides of the loop. The loop is placed in a homogeneous magnetic field with an induction $B={10}^{-1} \mathrm{T}$ directed at right angles to the plane of the drawing. A current $I=2\mathrm{A}$ is flowing in the loop. The period(in second) of small oscillations that the loop performers about its position of stable equilibrium is $T$, write the value of $10T$ to the nearest integer.

The value of earth magnetic field $B_H=0.3$ gauss. In this magnetic field a magnet is oscillating with $5$ oscillation/min. To increase the oscillation of magnet upto $10$ oscillation/min. The value of earth magnetic field increased by:

A Closely-wound solenoid of $1000$ turns and area of cross-section $2\times {10}^{-4}{\mathrm{m}}^2$ carries a current of $2.0$ ampere. It is placed with its horizontal axis at $30°$ with the direction of a uniform horizontal magnetic field of $0.16\mathrm{T}$ as shown in figure. What is the value of $\tau \times {10}^2$, where $\tau$ is torque (in SI unit) experienced by the solenoid?

A closely wound solenoid of $2000$ turns and area of cross-section $1.6\times {10}^{-4} {\mathrm{m}}^2$, carrying a current of $4.0 \mathrm{A}$, is suspended through its centre allowing it to turn in a horizontal plane. What is the torque(in SI unit) on the solenoid if a uniform horizontal magnetic field of $7.5\times {10}^{-2} \mathrm{T}$ is set up at an angle of $30°$ with the axis of the solenoid?

The coil is placed in a vertical plane and is free to rotate about a vertical axis which coincides with its diameter. A uniform magnetic field of $2 \mathrm{T}$ in the horizontal direction exists such that initially field is parallel to plane of coil. The coil rotates through an angle of $90°$ under the influence of the magnetic field when released from rest, then what is the angular speed(in $\mathrm{rad} {\mathrm{s}}^{-1}$) acquired by the coil when it has rotated by $90°$? The M.I. of the coil is $1\mathrm{kg} {\mathrm{m}}^2$ and magnetic moment of the coil is $4$ in SI unit.

Figure shows a small magnetised needle $A$ placed at a point, $O$, the arrow shows the direction of its magnetic moment. The other arrows show different positions (and orientation of the magnetic moment) of another identical magnetised needle $B$.

(i) In which configurations is the system not in equilibrium?

(ii) In which configuration is the system in stable, and unstable equilibrium?

(iii) Which configuration corresponding to the lowest potential energy among all the configurations shown?

A square cardboard of side $l$ and mass $m$ is suspended from a horizontal axis $XY$ as shown in figure. A single wire is wound along the periphery of board and carrying a clockwise current $I$. At $t=0$, a vertical downward magnetic field of induction $B$ is switched on. Find the minimum value of $B$ so that the board will be able to rotate up to horizontal level.

A negative charge is given to a nonconducting loop and the loop is rotated in the plane of paper about its centre as shown in figure. The magnetic field produced by the ring affects a small magnet placed above the ring in the same plane :

A stationary, circular wall clock has a face with a radius of $15 \mathrm{cm}$. Six turns of wire are wounded around its perimeter, the wire carries a current $2.0 \mathrm{A}$ in the clockwise direction. The clock is located, where there is a constant, uniform external magnetic field of $70 \mathrm{mT}$ (but the clock still keeps perfect time) at exactly $1:00 \mathrm{pm}$, the hour hand of the clock points in the direction of the external magnetic field

A single circular loop of radius $1.00 \mathrm{m}$ carries a current of $10.0 \mathrm{mA}$. It is placed in a uniform magnetic field of magnitude $0.500 \mathrm{T}$ that is directed parallel to the plane of the loop as suggested in the figure. The magnitude of the torque exerted on the loop by the magnetic field is.

Consider a triangular loop of wire with sides $a$ and $b$. The loop carries a current $I$ in the direction shown, and is placed in a uniform magnetic field that has magnitude $B$ and point in the same direction as the current in side $OM$ of the loop.

At the moment shown in the figure the torque on the current loop

A thin rectangular magnet, suspended freely, has a period of oscillation equal to $T$. Now, it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If it's period of oscillation is $T\text{'}$, then the ratio $\frac{T}{T\text{'}}$ is