The current associated with an electron of charge $e$ moving in a circular orbit of radius $r$ with speed $v$ around the positively charged nucleus is given by

$A$ $100$-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 $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

Write the unit and formula of the magnetic dipole moment due to a current-carrying loop.

The magnitude of magnetic induction at a point on the axis at a large distance $(r)$ from the centre of a circular coil of $n$ turns and area $A$ carrying current $I$ is given by:

$A$ straight wire carrying current $i$ is turned into a circular loop. If the magnitude of the magnetic moment associated with it in $MKS$ units is $M$,the length of the wire will be

$A$ uniform conducting wire of length $24a$ and resistance $R$ is wound up as a current-carrying coil in the shape of an equilateral triangle of side $a$ and then in the form of a square of side $a$. The coil is connected to a voltage source $V_{0}$. The ratio of the magnetic moment of the coils in the case of the equilateral triangle to that of the square is $1 : \sqrt{y}$, where $y$ is ..... .