University Physics Volume 2
University Physics Volume 2
18th Edition
ISBN: 9781938168161
Author: OpenStax
Publisher: OpenStax
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Chapter 14, Problem 14.1CYU

Check Your Understanding. A current I ( t ) = ( 5.0 A ) sin ( ( 200 π r a d / s ) t ) flows through the solenoid of part (b) of Example 14.1. What is the maximum emf induced in the surrounding coil?

Expert Solution & Answer
Check Mark
To determine

The maximum emf induced in the surrounding coil.

Answer to Problem 14.1CYU

The maximum emf induced in the surrounding coil is 4.56×10-2volt.

Explanation of Solution

Given info:

  N1=500turns

  N2=10turns

  R1=3.10cm = 0.0310 m

  l1=75cm = 0.750 m

  I(t)=(5.0A)sin((120πrad/s)t)

Formula used:

The formula for calculating induced emf in a surrounding coil is:

  ε=MdI1dt volt....... (1)

Here, M is mutual inductance and M=μoN1N2πR12l1....... (2)

Calculation:

From equation (2) we get,

  M=μoN1N2πR12l1=( 4π× 10 7 H/m)×500×10×3.14× ( 0.0310m )20.750m=2.53×105H

Now, the emf induced in the surrounding coil is,

  ε=MdI1dt(takingthemagnitudeonly)=(2.53× 10 5H)×ddt[(5.0A)sin((120πrads)t)]=(2.53× 10 5)×(5.0A)×(120π)×cos(120πrads)=2.53×105×1802.67=0.0456=4.56×10-2volt

Conclusion:

The maximum emf induced in the surrounding coil is 4.56×10-2volt.

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Chapter 14 Solutions

University Physics Volume 2

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