Moving Charges and Magnetism - Result Question 15

15. 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

[2005]

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

(b) $\frac{B}{v}$

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

(d) $\frac{v}{B}$

Show Answer

Answer:

Correct Answer: 15. (c)

Solution:

  1. (c) Magnetic field produced by moving electron in circular path

$ B=\frac{\mu_o i}{2 r} $

Here, $i=$ current

$r=$ radius of circular path

But $i=\frac{q}{t}=\frac{q}{2 \pi r} v \quad[\because t=\frac{\text{ Distance }}{\text{ Velocity }}=\frac{2 \pi r}{v}]$

$\therefore \quad$ Manetic field at centre, $B=\frac{\mu_o}{2 r} \times \frac{q v}{2 \pi r}$

$ \Rightarrow B=\frac{\mu_o q v}{4 \pi r^{2}} \Rightarrow r \propto \sqrt{\frac{V}{B}} $