$A$ 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 free to turn in a uniform magnetic field. The loop will come into equilibrium when its plane is inclined at

$A$ 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

$A$ galvanometer coil has $500$ turns and each turn has an average area of $3 \times 10^{-4} \ m^{2}$. If a torque of $1.5 \ Nm$ is required to keep this coil parallel to the magnetic field when a current of $0.5 \ A$ is flowing through it,the strength of the magnetic field (in $T$) is:

$A$ 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).

$A$ current-carrying coil is subjected to a uniform magnetic field. The coil will orient itself so that its plane becomes