The relation between magnetic moment $(M)$ of a current-carrying circular coil and the length $(L)$ of the wire used is:

Magnetic field at the centre of a circular loop of area $A$ is $B$. The magnetic moment of the loop will be ($\mu_{0} =$ permeability of free space).

$A$ steady current $i$ flows in a small square loop of wire of side $L$ in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let $\overrightarrow {{\mu _1}} $ and $\overrightarrow {{\mu _2}} $ respectively denote the magnetic moments due to the current loop before and after folding. Then

The magnetic dipole moment of a rectangular current-carrying loop is:

The dipole moment of a circular loop carrying a current $I$ is $m$ and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant,the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is

In a hydrogen atom,the electron moves around the nucleus in an orbit of radius $5 \times 10^{-11} \ m$. Its time period is $1.5 \times 10^{-16} \ s$. The current associated with the electron motion is $........$ (charge of electron is $1.6 \times 10^{-19} \ C$)