$A$ circular loop and a square loop are formed from two wires of same length and cross-section. The same current is passed through them. The ratio of their dipole moments is

Two particles each of mass $m$ and charge $q$ are attached to the two ends of a light rigid rod of length $2R$. The rod is rotated at a constant angular speed $\omega$ about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is:

$A$ charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to the normal axis,then the magnetic moment of the loop is:

$A$ current-carrying loop consists of $3$ identical quarter circles of radius $R$,lying in the positive quadrants of the $xy$,$yz$,and $zx$ planes with their centers at the origin,joined together. Find the direction and magnitude of the magnetic field $\vec{B}$ at the origin.

$A$ small bar magnet experiences a torque of $0.016 \ Nm$ when placed with its axis at $30^{\circ}$ with an external magnetic field of $0.04 \ T$. If the bar magnet is replaced by a solenoid of cross-sectional area $1 \ cm^2$ and $1000$ turns,having the same magnetic moment as that of the bar magnet,then the current flowing through the solenoid is: (in $A$)

$A$ thin circular wire carrying a current $I$ has a magnetic moment $M$. The shape of the wire is changed to a square and it carries the same current. It will have a magnetic moment