Tutorials in Introductory Physics
Tutorials in Introductory Physics
1st Edition
ISBN: 9780130970695
Author: Peter S. Shaffer, Lillian C. McDermott
Publisher: Addison Wesley
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Chapter 22.2, Problem 1aTH

On the two diagrams below, indicate the direction of the induced current in the loop at each of the instants shown. If the current is zero, state that explicitly. Explain how you determined your answers.

Chapter 22.2, Problem 1aTH, On the two diagrams below, indicate the direction of the induced current in the loop at each of the
Expert Solution & Answer
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To determine

The direction of the induced current in the loop at each instant.

Explanation of Solution

Introduction:

Write the expression to calculate the magnetic flux.

  ϕ=BScosθ=BScosωt

Here, ϕ is the magnetic flux, B is the magnetic field, S is the surface area, θ is the angle, ω is the angular speed and t is the time.

Write the expression to calculate induced emf.

  e=dϕdt

Here, e is the emf.

Case 1:

Consider time 1.

Calculate the magnetic flux.

  ϕ=BScos90°=BS(0)=0

The magnetic flux will decrease as the angle reaches to 90° .

Calculate the induced emf.

  e=dϕdt=d( BScos( ωt ))dt=BSωsin(ωt)

The emf will increase which leads to the increase of current. The coil will produce a magnetic field in the same direction. According to Lenz’s law the direction of current will be anticlockwise when seen from the left side of the loop.

Case 2:

Calculate the magnetic flux.

  ϕ=BScos0°=BS(1)=BS

The magnetic flux will decrease as the angle reaches to 90° .

Calculate the induced emf.

  e=dϕdt=d( BScosθ)dt=0

The emf is zero.

Calculate the current.

  I=eR=0R=0

For the time 2, the emf induced will be zero which will lead to zero current in the loop.

Conclusion:

Therefore, for time 1 the current will be in anticlockwise direction and for time 2 the current is zero.

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