Concept explainers
(a)
The magnitude of the induced current in the wire.
(a)
Answer to Problem 31.20P
The magnitude of the induced current in the wire is
Explanation of Solution
Given info: The radius of the upper circle is
Write the expression for the area of the loop.
Here,
For upper circle.
Substitute
Thus, the area of the upper circle is
For lower circle.
Substitute
Thus, the area of the lower circle is
Write the expression for the magnetic flux through a coil
Here,
Write the expression for the emf of the coil.
Here,
Substitute
For the upper circle.
Substitute
Thus, the emf induced in the upper loop is
For the lower circle.
Substitute
Thus, the emf induced in the upper loop is
Write the expression for the resistance.
Here,
For upper circle.
Substitute
Thus, the resistance in the upper circle is
For lower circle.
Substitute
Thus, the resistance in the lower circle is
Write the expression for the induced current.
Substitute
Conclusion:
Therefore, the magnitude of the induced current in the wire is
(b)
The direction of the induced current in the wire.
(b)
Answer to Problem 31.20P
The current is clockwise in the upper loop and the current is counterclockwise in the lower loop
Explanation of Solution
Given info: The radius of the upper circle is
Write the expression for the induced current in the wire.
Consider negative current as clockwise and positive current as counterclockwise.
From the above expression, the induced current is directly proportional to the induced emf. From part (a), the value of the induced emf for upper loop is negative, so the value of the current is also negative. The negative current shows the current is clockwise in the upper loop. And also from part (a), the value of the induced emf for lower loop is positive, so the value of the current is also positive. The positive current shows the current is counterclockwise in the lower loop. Thus, the current is clockwise in the upper loop and the current is counterclockwise in the lower loop.
Conclusion:
Therefore, the current is clockwise in the upper loop and the current is counterclockwise in the lower loop.
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Chapter 31 Solutions
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