First slide

Induced Electric Field and Magnetic field

Question

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

Difficult

A

$π V / m$
B

10 V/m
C

2 V/m
D

62 V/m

Solution

From Faraday's law of electromagnetic induction, the induced emf is equal to negative rate of change of magnetic flux.
That is $e = - \frac{Δϕ}{Δt}$
Flux induced $= 2 BA cosθ$
where B is magnetic field, A is area.
$Given, θ = 0^{\circ}, Δt = \frac{1}{100} s$
$Δϕ = 2 \times 0 .01 \times π \times (1)^{2} \times 200 \times \cos 0^{\circ}$
$∴ e = \frac{- 2 \times 0 .01 \times π \times (1)^{2} \times 200}{100} = - 4 π volt$
Circumference of a circle of radius $r is 2 πr .$
$∴$ Induced electric field E is
$E = \frac{| e |}{2 πr} = \frac{4 π}{2 πr} = \frac{2}{1} = 2 V / m$

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