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Problem 8.1316 A very long solenoid of radius a, with n turns per unit length, carries a current I,. Coaxial with the solenoid, at radius b≫a, is a circular ring of wire, with resistance R. When the current in the solenoid is (gradually) decreased, a current I, is induced in the ring. (a) Calculate I,, in terms of dl,/dt. (b) The power (IR) delivered to the ring must have come from the solenoid. Con- firm this by calculating the Poynting vector just outside the solenoid (the elec- tric field is due to the changing flux in the solenoid; the magnetic field is due to the current in the ring). Integrate over the entire surface of the solenoid, and check that you recover the correct total power.

Problem 8.1316 A very long solenoid of radius a, with n turns per unit length, carries a current I,. Coaxial with the solenoid, at radius b≫a, is a circular ring of wire, with resistance R. When the current in the solenoid is (gradually) decreased, a current I, is induced in the ring. (a) Calculate I,, in terms of dl,/dt. (b) The power (IR) delivered to the ring must have come from the solenoid. Con- firm this by calculating the Poynting vector just outside the solenoid (the elec- tric field is due to the changing flux in the solenoid; the magnetic field is due to the current in the ring). Integrate over the entire surface of the solenoid, and check that you recover the correct total power.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Problem 8.1316 A very long solenoid of radius a, with n turns per unit length, carries a current I,. Coaxial with the solenoid, at radius b≫a, is a circular ring of wire, with resistance R. When the current in the solenoid is (gradually) decreased, a current I, is induced in the ring. (a) Calculate I,, in terms of dl,/dt. (b) The power (IR) delivered to the ring must have come from the solenoid. Con- firm this by calculating the Poynting vector just outside the solenoid (the elec- tric field is due to the changing flux in the solenoid; the magnetic field is due to the current in the ring). Integrate over the entire surface of the solenoid, and check that you recover the correct total power.
Transcribed Image Text:Problem 8.1316 A very long solenoid of radius a, with n turns per unit length, carries a current I,. Coaxial with the solenoid, at radius b≫a, is a circular ring of wire, with resistance R. When the current in the solenoid is (gradually) decreased, a current I, is induced in the ring. (a) Calculate I,, in terms of dl,/dt. (b) The power (IR) delivered to the ring must have come from the solenoid. Con- firm this by calculating the Poynting vector just outside the solenoid (the elec- tric field is due to the changing flux in the solenoid; the magnetic field is due to the current in the ring). Integrate over the entire surface of the solenoid, and check that you recover the correct total power.
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