First slide

Magnetic field due to a moving charge

Question

An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is proportional to

Moderate

A

$\frac{B}{v}$
B

$\frac{v}{R}$
C

$\sqrt{\frac{v}{B}}$
D

$\sqrt{\frac{B}{v}}$

Solution

Electric current corresponding to the revolution of electron is $i = \frac{ev}{2 πr}$ . Magnetic field due to circular current at the centre is $B = \frac{μ_{0}}{4 π} . \frac{2 πi}{r} = \frac{μ_{0}}{4 π} . \frac{ev}{r^{2}} \Rightarrow$ $r = \sqrt{\frac{μ_{0}}{4 π} . \frac{ev}{B}} \Rightarrow r \propto \sqrt{\frac{v}{B}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App