First slide

Magnetic field due to a current carrying circular ring

Question

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

Moderate

A

$\frac{μ_{0} n^{2} e}{r}$
B

$\frac{μ_{0} n e}{2 r}$
C

$\frac{μ_{0} n e}{2 π r}$
D

Zero

Solution

$Current in the orbit, I = \frac{e}{T}$
$I = \frac{e}{(2 π / ω)} = \frac{ω e}{2 π} = \frac{(2 π n) e}{2 π} = n e$
Magnetic field at centre of current carrying circular coil is given by
$B = \frac{μ_{0} I}{2 r} = \frac{μ_{0} n e}{2 r}$

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