The magnetic dipole moment of a current loop is independent of

$A$ uniform conducting wire of length $12 a$ 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 $a$.
The magnetic dipole moments of the coil in each case respectively are:

$A$ circular and a square coil are prepared from two identical metal wires and a current is passed through them. The ratio of the magnetic dipole moment associated with the circular coil to that with the square coil is

An insulating thin rod of length $l$ has a linear charge density $\rho(x) = \rho_0 \frac{x}{l}$ on it. The rod is rotated about an axis passing through the origin $(x = 0)$ and perpendicular to the rod. If the rod makes $n$ rotations per second,then the time-averaged magnetic moment of the rod is:

The ratio of the magnetic field and the magnetic moment at the centre of a current-carrying circular loop is $x$. When both the current and the radius are doubled, the ratio will be:

What is the magnetic dipole moment for a coil? Write its $SI$ unit and dimensional formula,and explain its stable and unstable equilibrium.