2005 AIPMT Moving Charges and MagnetismMagnetic Field due to a Circular Coil Medium Question 14 of 15 in Magnetic Field due to a Circular Coil

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 :

A $\sqrt{\dfrac{v}{B}}$
B $\dfrac{v}{B}$
C $\sqrt{\dfrac{B}{v}}$
D $\dfrac{B}{v}$

The answer is A.

Solution

The revolving electron is equivalent to a current $I = \dfrac{e}{T}$, where the time period is $T = \dfrac{2\pi R}{v}$.
$I = \dfrac{ev}{2\pi R}$
Magnetic field at the centre of a circular current: $B = \dfrac{\mu_0 I}{2R}$
$B = \dfrac{\mu_0}{2R}\left(\dfrac{ev}{2\pi R}\right) = \dfrac{\mu_0 ev}{4\pi R^2}$
$\Rightarrow R^2 = \dfrac{\mu_0 ev}{4\pi B}$
$\Rightarrow R \propto \sqrt{\dfrac{v}{B}}$

Concept Field of a revolving charge

Magnetic Field due to a Circular Coil in past papers

15 questions from this chapter have appeared across 12 exam years.