Concept explainers
(a)
The current induced in the aluminum ring
(a)
Answer to Problem 5P
A current of
Explanation of Solution
Write the equation for the emf generated in the coil.
Here,
Here,
Write the equation for the magnetic field due to the solenoid.
Here,
Substitute
Write the equation for the area of the coil.
Here,
Substitute equation (VI) in equation (V).
The ring is placed at one end of a solenoid. The field in the end of the solenoid is half the field at the center of the solenoid. Write the equation for the emf induced in the ring.
Substitute
Write the equation for the current induced in the ring.
Conclusion:
Substitute
Therefore, the current induced in the ring is
(b)
The magnitude of magnetic field in the ring
(b)
Answer to Problem 5P
The induced current produces a magnetic field of
Explanation of Solution
Write the equation for the magnetic field produced in the ring.
Here,
Conclusion:
Substitute
Therefore, the induced current produces a magnetic field of
(c)
The direction of magnetic field in the ring
(c)
Answer to Problem 5P
The magnetic field in the ring points towards the left
Explanation of Solution
Figure (I) shows the direction of the magnetic field in the solenoid.
The magnetic field of the solenoid points to the right as shown in figure.1. Therefore, the magnetic field at the center of the ring acts towards the left in order to oppose the increasing field.
Conclusion:
Therefore, the magnetic field in the ring acts towards the left.
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Chapter 23 Solutions
Principles of Physics: A Calculus-Based Text
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