Two single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. (a) Show that the mutual inductance of the pair is approximately M = μ0πr2/2R. (b) Evaluate M for r = 2.00 cm and R = 20.0 cm.

Two single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. (a) Show that the mutual inductance of the pair is approximately M = μ0πr2/2R. (b) Evaluate M for r = 2.00 cm and R = 20.0 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

Chapter23: Faraday’s Law And Inductance

Section: Chapter Questions

Problem 67P

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Concept explainers

Voltage Across Inductor

An actor is a passive electrical component that consists of a coil bent in the form of wire which uses electromagnetism to produce electric current through the coil. When the electric current flows through a conductor that is the coil, a magnetic flux is developed around the conductor. This flow of current through the coil creates a magnetic field based on Fleming's Right-hand thumb rule. If there is any decrease in the current passing through the inductor, then the magnetic field will also decrease and energy is released through the generation of electric current. There is also a secondary voltage inducing in the same coil due to the magnetic flux, since it opposes any changes in the electric current flowing through the circuit. An inductor is also called choke, coil, or solenoid. A choke is designed to block certain frequencies when the DC current passes. A winding coil is coated with insulation to give extra insulation and protect the circuit. They are usually tightly wrapped around a central core which is cylindrical in nature so that the magnetic flux can be induced. The solenoid is a three-dimension coil that is used to exhibit electromagnetism when the magnetic field is developed due to the current flowing through the coil. The sign convention of the inductor is the same as the power dissipating device. When the current flows into the positive side of the voltage across the inductor, the value is positive and the inductor dissipates power whereas when the inductor releases the power back to the circuit, the current has a negative sign convention. 

Question

Two single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. (a) Show that the mutual inductance of the pair is approximately M = μ₀πr²/2R. (b) Evaluate M for r = 2.00 cm and R = 20.0 cm.

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