An electron is rotating in a circular orbit with angular speed co. Radius of the circle is R.

Options

A. Magnetic field at the centre of the circle is zero
B. Equivalent current is `(e omega)/(2pi)`
C. Magnetic dipole moment is `1/2 e omega R^(2)`
D. Magnetic field at the centre is `(mu_(0)e omega)/(4 pi R)`

Answer

b, c, d

Explanation

Rotating electron is like an electric current Equivalent current can be written as follows:
`i = e/(2 pi // omega) = (e omega)/(2 pi)`
Magnetic moment of a loop is defined as current multiplied with the area, hence
Magnetic moment of electron ` = i pi R^(2) = (e omega)/(2 pi) pi R^(2) = 1/2 eomega R^(2)`
We can treat it like a circular loop of current and can find magnetic field `(B = (mu_(0)i)/(2R))` at its centre .
`B = (mu_(0)i)/(2R) = (mu_(0) (e omega)/(2 pi))/(2R) = (mu_(0) e omega)/(4 pi R)`
using the same formula for magnetic field its centre. Hence we can see that options (b), (c) and (d) are correct.