An electron moves with a constant speed $v$ along a circle of radius $r$. Its magnetic moment will be ($e$ is the electron's charge).

Magnetic induction at the centre of a circular loop of area $\pi \ m^2$ is $0.1 \ T$. The magnetic moment of the loop is ( $\mu_0 = \text{permeability of air}$ ).

Two thick wires and two thin wires,all of the same material and same length,form a square in three different ways $P, Q,$ and $R$ as shown in the figure with the current connection indicated. The magnetic field at the centre of the square is zero in cases:

The number of turns of two circular coils $A$ and $B$ are $300$ and $200$ respectively. The magnetic moments of the two coils $A$ and $B$ are in the ratio $1:2$. If the two coils carry equal currents, then the ratio of radii of coils $A$ and $B$ is

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

$A$ $100$-turn closely wound circular coil of radius $5 \text{ cm}$ has a magnetic field of $3.14 \times 10^{-3} \text{ T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively: (Take $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)