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.
Glencoe Physics: Principles and Problems, Student Edition
1st Edition
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Paul W. Zitzewitz
Chapter25: Electromagnetic Induction
Section: Chapter Questions
Problem 48A
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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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