An electron moving in a circular orbit of radius `r` makes `n` rotation per secound. The magnetic field produced at the centre has magnitude

Options

A. zero
B. `(mu_0n^2e)/(r)`
C. `(mu_0"ne")/(2r)`
D. `(mu_0"ne")/(2pir)`

Answer

C

Explanation

Current due to orbital motion of electron is
`I=("charge")/("time period")=(e)/(1//n)=n e`
Magnetic field due to circular motion of electron is
`B=(mu_0)/(4pi)(2pinI)/(r)=(mu_0nI)/(2r)=(mu_0I)/(2r)`
where n is number of loops. Here `n=1`, as electron is making one loop.
`B=(mu_0)/(2r)("ne")=(mu_0"ne")/(2r)`