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Question

A 50turns circular coil has a radius of 3cm, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B increased from 0.10tesla to 0.35tesla in 2milliseconds. The average induced e.m.f. in the coils is


A

1.77volts

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B

17.7volts

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C

177volts

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D

0.177volts

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Solution

The correct option is B

17.7volts


Step 1: Given data

No. of turns in the coil, N=50

Radius of the circular coil, r=3cm

=3×10-2mAs1m=102cm

Initial value of magnetic field, B1=0.10Tesla

Final value of magnetic field, B2=0.35Tesla

Time interval, T=2ms

=2×10-3s

Step 2: Find the magnetic flux, ϕ

The initial value of flux, ϕ1=NB1A

The final value of flux, ϕ2=NB2A

Step 3: Find the value of induced emf, e

Value of induced emf, e=(NB1ANB2A)/t

=(NA/t)[B2B1]=N×π×r2/tB2-B1=50×3.14×3×10-320.35-0.10=17.675Volts=17.7V

Hence, option (B) is correct.


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