Answered: An aluminum ring of radius r₁=5.00 cm…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Magnetic Forces And Magnetic Fields

Section: Chapter Questions

Problem 58P: A solenoid 10.0 cm in diameter and 75.0 cm long is made from copper wire of diameter 0.100 cm, with...

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An aluminum ring of radius

r₁ = 5.00 cm

and a resistance of 4.15 10^-4 Ω is placed around one end of a long air-core solenoid with 930 turns per meter and radius

r₂ = 3.00 cm

as shown in the figure below. 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 wire is wrapped several times around a horizontal cylinder of radius r₂, creating a long solenoid. Current I flows out of the page as the turns of wire wrap above the central axis of the cylinder, then down the front of the cylinder, and into the page as they wrap below the central axis. A short ring of radius r₁ > r₂ is coaxial with the solenoid and encircles its left end.

(a) What is the induced current in the ring?
A

(b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the ring?
µT

(c) At the center of the ring, what is the direction of the magnetic field produced by the induced current in the ring?

to the leftto the right upwarddownward

An aluminum ring of radius r₁ = 5.00 cm and a resistance of 4.15 × 10-4 № is placed around one end of a long air-core
solenoid with 930 turns per meter and radius r₂ = 3.00 cm as shown in the figure below. 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.
0
(a) What is the induced current in the ring?
A
(b) At the center of the ring, what is the magnitude of the magnetic field produced by the induced current in the
ring?
μT
(c) At the center of the ring, what is the direction of the magnetic field produced by the induced current in the ring?
to the left
O to the right
O upward
downward

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