Question

A charge $e$ moves round a circle of radius $r$ with a uniform speed $v$. The magnitude of the magnetic induction at the centre of the circle is

• A. $\frac{{\mu }_{0}ev}{4\pi r}$
• B. $\frac{{\mu }_{0}ev}{4\pi r^2}$
• C. $\frac{{\mu }_{0}ev}{4\pi r^3}$
• D. $\frac{{\mu }_{0}ev}{4\pi rv}$

Answer 1

Answer: (B)

$\frac{{\mu }_{0}ev}{4\pi r^2}$

$Current=\frac{\Delta Q}{\Delta t}=\frac{eV}{2\pi r}$
magnetic field due to loop of radius $r$ carrying current $i$ at center is

$\therefore B=\frac{{\mu }_{o}i}{2r}$
$=\frac{eV{\mu }_o}{4\pi r^2}$