$A$ circular coil carrying a current of $2.5 \ A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is $10 \ A$, the time period of oscillation is:

$A$ current-carrying loop is placed in a uniform magnetic field in four different orientations,$I$,$II$,$III$,and $IV$. Arrange them in the decreasing order of potential energy.

$A$ square coil of side $10 \ cm$ having $200$ turns is placed in a uniform magnetic field of $2 \ T$ such that the plane of the coil is in the direction of the magnetic field. If the current through the coil is $3 \ mA$, then the torque acting on the coil is

$A$ circular coil carrying a current of $2.5 \ A$ is free to rotate about an axis in its plane perpendicular to an external magnetic field. When the coil is made to oscillate, the time period of oscillation is $T$. If the current through the coil is $10 \ A$, the time period of oscillation is

Derive an expression for the torque acting on a current-carrying loop which subtends an angle $\theta$ with a uniform magnetic field.

The given figure shows the north and south poles of a permanent magnet in which a coil of $n$ turns of cross-sectional area $A$ is placed. When a current $I$ is passed through the coil,the plane of the coil makes an angle $\theta$ with respect to the direction of the magnetic field $B$. If the plane of the magnetic field and the coil are horizontal and vertical respectively,the torque on the coil will be