An electron is moving in a circular orbit of radius R with an ang… - Vidyadip

MCQ

An electron is moving in a circular orbit of radius $R$ with an angular acceleration $\alpha$ . At the centre of the orbit is kept a conducting loop of radius $r, (r < < R).$ The $e.m.f$ induced in the smaller loop due to the motion of the electron is

A
zero, since charge on electron in constant
✓
$\frac{{{\mu _0}e{r^2}}}{{4R}}\alpha $
C
$\frac{{{\mu _0}e{r^2}}}{{4\pi R}}\alpha $
D
none of these

✓

Answer

Correct option: B.

$\frac{{{\mu _0}e{r^2}}}{{4R}}\alpha $

b
$i=\frac{e \omega}{2 \pi} \dots(1)$

$B=\frac{\mu_{0}}{4 \pi} \frac{2 i}{R}=\frac{\mu_{0} i}{2 R} \dots(2)$

From $(1)$ and $(2)$

$\phi=B A=\frac{\mu_{0} i}{2 R} \cdot \pi r^{2}=\frac{\mu_{0} \pi r^{2}}{2 R} \cdot \frac{e \omega}{2 \pi}$

$e=B A=\frac{\mu_{0} r^{2} e}{4 \pi} \frac{d \omega}{d t}=\frac{\mu_{0} r^{2} e \alpha}{4 R}$

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