(a)
The induced current in the ring.
(a)
Answer to Problem 11P
The induced current in the ring is
Explanation of Solution
Write the expression to calculate the magnetic flux through the loop.
Here,
Write the expression for the induced emf by Faraday law.
Here,
Write the expression for the area.
Here,
Write the expression for the magnetic field.
Here,
Substitute
Write the expression for the induced current.
Substitute
Conclusion:
Substitute
The direction of the current is counter clockwise.
Therefore, the induced current in the ring is
(b)
The magnitude of the magnetic field at the center of the ring
(b)
Answer to Problem 11P
The magnitude of the magnetic field at the center of the ring is
Explanation of Solution
Write the expression to calculate the magnetic field at the center of the ring.
Here,
Conclusion:
Substitute
Therefore, the magnitude of the magnetic field at the center of the ring is
(c)
The direction of the magnetic field at the center of the ring.
(c)
Answer to Problem 11P
The direction of the magnetic field at the center of the ring is to the left.
Explanation of Solution
The magnetic field of the solenoid points towards the right but the induced field opposes the original field. So, the magnetic field at the center of the ring will be directed towards the left.
Conclusion:
Therefore, the direction of the magnetic field at the center of the ring is to the left.
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Chapter 31 Solutions
Physics for Scientists and Engineers With Modern Physics
- An aluminum ring of radius r1 = 5.00 cm and resistance 3.00 104 is placed around one end of a long air-core solenoid with 1 000 turns per meter and radius r2 = 3.00 cm as shown in Figure P30.5. Assume the axial component of the field produced by the solenoid is one-half as strong over the area of the end of the solenoid as at the center of the solenoid. Also assume the solenoid produces negligible field outside its cross-sectional area. The current in the solenoid is increasing at a rate of 270 A/s. (a) What is the induced current in the ring? At the center of the ring, what are (b) the magnitude and (c) the direction of the magnetic field produced by the induced current in the ring? Figure P30.5 Problems 5 and 6.arrow_forwardA solenoid has a ferromagnetic core, n = 1000 turns per meter, and I = 5.0 A. If B inside the solenoid is 2.0 T, what is for the core material?arrow_forwardA wire is bent in the form of a square loop with sides of length L (Fig. P30.24). If a steady current I flows in the loop, determine the magnitude of the magnetic field at point P in the center of the square. FIGURE P30.24arrow_forward
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