$A$ thin magnetic needle is placed in a magnetic field of $200 \ G$ with its axis at $30^{\circ}$ to the direction of the field. Find the magnetic moment of the needle if it experiences a torque of $0.012 \ Nm$ in this field. (in $Am^2$)

$A$ current-carrying loop is placed in a uniform magnetic field $B$ in different orientations $I$, $II$, $III$, and $IV$ as shown in the figure. The correct order of decreasing potential energy is ($\hat{n}$ is the unit vector normal to the plane of the loop).

Current $I$ is carried in a wire of length $L$. If the wire is bent into a circular coil of single turn,the maximum torque in a given magnetic field $B$ is:

$A$ coil carrying electric current is placed in a uniform magnetic field,then

$A$ $100$ turns coil shown in the figure carries a current of $2\, A$ in a magnetic field $B = 0.2\, Wb/m^2$. The torque acting on the coil is

$A$ coil having $10 \text{ A m}^2$ magnetic moment is placed in a vertical plane and is free to rotate about its horizontal axis, which coincides with its diameter. $A$ uniform magnetic field of $2 \text{ T}$ in the horizontal direction exists such that initially the axis of the coil is in the direction of the field. The coil rotates through an angle of $90^{\circ}$ under the influence of the magnetic field. The moment of inertia of the coil is $0.1 \text{ kg m}^2$. What will be its angular speed (in $\text{ rad/s}$)?