$A$ closely wound solenoid of $800$ turns and area of cross section $2.5 \times 10^{-4} \text{ m}^2$ carries a current of $3.0 \text{ A}$. The magnetic moment associated with it is . . . . . . . (in $\text{ JT}^{-1}$)

$A$ uniform conducting wire of length $12a$ and resistance $R$ is wound up as a current-carrying coil in the shape of:
$(i)$ an equilateral triangle of side $a$;
$(ii)$ a square of side $a$;
$(iii)$ a regular hexagon of side $a$.
The coil is connected to a voltage source $V_{0}$. Find the magnetic moment of the coils in each case.

$A$ current-carrying circular loop is freely suspended by a long thread. The plane of the loop will point in the direction:

Two wires of the same length are used to form a circle and a square. They carry the same current. The ratio of the magnetic moment of the circle to that of the square is:

The magnetic field at the centre of a single-turn circular coil of a given length of wire carrying a current $I$ is $B$. If the same wire is bent into a circular coil of two turns and the same current $I$ is passed through it,the new magnetic field at the centre will be:

An electron revolving in a circular orbit of radius $r$ with velocity $v$ and frequency $f$ has an orbital magnetic moment $M$. If the frequency of revolution is doubled,then the new magnetic moment will be: