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:

• A. $\frac{B}{v}$
• B. $\frac{v}{B}$
• C. $\sqrt{\bigg(\frac{v}{B}\bigg)}$
• D. $\sqrt{\bigg(\frac{B}{v}\bigg)}$

Answer 1

Answer: (C)

$\sqrt{\bigg(\frac{v}{B}\bigg)}$

Answer 2

Centripetal force is provided by magnetic force.
Fcentripetal = Fmagnetic

​∴$\frac{mv^2}{r}$ =qvB

r = $\frac{mv}{qb}$

$\Rightarrow$ r $\propto \, \frac{v}{B}$

since$\frac{m}{q}$ is constant

Correct option is (C): $\sqrt{\bigg(\frac{v}{B}\bigg)}$