First slide

Magnetic field due to a current carrying circular ring

Question

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

Moderate

A

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

$\frac{v}{B}$
C

$\frac{B}{v}$
D

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

Solution

Magnetic field due to circular current carrying ring= $\frac{μ_{o} i}{2 R}$
Current i= $\frac{q v}{2 πr}$
B= $\frac{μ_{o} q v}{4 {πr}^{2}}$
Thus r $α \sqrt{\frac{v}{B}}$

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