First slide

Induced Electric Field and Magnetic field

Question

A conducting ring of radius 1 m is placed in an uniform magnetic field B of 0.01 T oscillating with frequency 100 Hz with its plane at right angles to B. What will be the induced electric field?

Difficult

A

$π V / m$
B

2 V/m
C

10 V/m
D

62 V/m

Solution

In a constant magnetic field, conducting ring oscillates with a frequency of 100 Hz.
i.e., $T = \frac{1}{100} s,$ in time $\frac{T}{2}$ flux links with coil changes from BA to zero.
$\Rightarrow Induced emf, e = \frac{Change in flux}{Time}$
$= \frac{B A}{T / 2} = \frac{2 B A}{T} = \frac{2 B \times π r^{2}}{T} = \frac{2 \times 0.01 \times π \times 1^{2}}{1 / 100} = 4 π V$
Induced electric field along the circle, using Maxwell equation $∮ E . dl = - \frac{dϕ}{dt} = - A \frac{dB}{dt} = e$
$\Rightarrow E = \frac{1}{2 πr} \times ({πr}^{2} \times \frac{dB}{dt}) = \frac{e}{2 πr} = \frac{4 π}{2 πr} = 2 V / m$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App