First slide

Faraday's law of Electromagnetic induction

Question

Find the average induced voltage in a coil of an area 500 cm² and having 1000 turns, when it is turned through 180⁰ in 0. 1 s. It is also given that the coil is initially placed perpendicularly to a uniform field of 0.4 gauss.

Difficult

A

0.02 V
B

0.04 V
C

1.4 V
D

0.08 V

Solution

Here, $A = 500 {cm}^{2} = 500 \times 10^{- 4} m^{2}$
$N = 1000, B = 0 .4 G = 0 .4 \times 10^{- 4} T$
$t = \frac{1}{10} s$
When the coil is held perpendicular to the filed, the normal to the plane of the coil makes an angle of 0⁰ with the field B.
$∴ Initial flux, ϕ_{1} = BAcos 0^{\circ} = BA$
$final flux, ϕ_{2} = BAcos 180^{\circ} = - BA$
Average induced emf,
$ε = - N (\frac{ϕ_{2} - ϕ_{1}}{t}) = - N (\frac{- BA - BA}{t})$
$= \frac{2 NBA}{t} = \frac{2 \times 1000 \times 0 .4 \times 10^{- 4} \times 500 \times 10^{- 4}}{1 / 10}$
= 0.04 V

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