The difference between the two rotations and check whether they are indistinguishable.
Answer to Problem 62PQ
When the coil is parallel to the field and is rotated to a position where it is perpendicular to the field, the emf induced is found to be negative. The emf is found to be positive, when the coil is rotated back to its initial position. Both the rotations are distinguishable.
Explanation of Solution
Faraday’s law states that, when the magnetic flux changes an emf is induced in the coil.
The direction of the induced emf is given by Lenz law. Lenz law states that the change in flux is opposed by the current induced in the circuit due to a change in magnetic field. The current induced in the circuit, exerts a mechanical force as well.
Write the expression for induced emf from Faraday’s and Lenz law.
Here,
Write the expression for magnetic flux.
Here,
Write the expression for magnitude of the vector
Here,
Write the expression for magnitude of the magnetic flux.
Here,
Write the expression for initial flux linked with the coil.
Here,
Substitute
Write the expression for final flux linked with the coil.
Here,
Substitute
Substitute
Write the equation for change in magnetic flux.
The coil is now rotated back to its initial position. The coil now rotates from the position where the magnetic flux linked with it is
Therefore,
Write the expression for induced emf due to second rotation.
Conclusion:
Substitute
Substitute
Substitute
Therefore, the current in the coil flows in the counter clockwise direction.
Substitute
The induced current flows in the clockwise direction.
Therefore, when the coil is parallel to the field and is rotated to a position where it is perpendicular to the field, the emf induced is found to be negative. The emf is found to be positive, when the coil is rotated back to its initial position. Both the rotations are distinguishable.
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Chapter 32 Solutions
Physics for Scientist and Engineers (Foundations And Connection; Volume I and II) LLF edition
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