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:
- (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}} $
