College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
Mutual inductance is the phenomenon where a change in current in one coil induces an electromotive force (EMF) in a nearby coil. It is quantified by the mutual inductance coefficient, $M$, which depends on the geometry and orientation of the coils.
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The mutual inductance between two coils can be calculated using $M = \frac{N_2 \Phi_{21}}{I_1}$, where $N_2$ is the number of turns in coil 2, $\Phi_{21}$ is the magnetic flux through coil 2 due to current $I_1$ in coil 1.
The induced EMF in coil 2 due to a changing current in coil 1 is given by Faraday's law: $\mathcal{E}_2 = -M \frac{dI_1}{dt}$.
Mutual inductance is symmetrical, meaning that $M_{12} = M_{21}$.
The mutual inductance can be increased by increasing the number of turns, placing the coils closer together, or using materials with higher magnetic permeability.
Review Questions
What unit is used to measure mutual inductance?
How does Faraday's law relate to mutual inductance?
List three ways to increase mutual inductance between two coils.
Related terms
Electromotive Force (EMF): The voltage generated by a changing magnetic field or by moving a conductor through a magnetic field.
Faraday's Law of Induction: $\mathcal{E} = -\frac{d\Phi_B}{dt}$; it states that the induced EMF in any closed circuit is equal to the negative rate of change of the magnetic flux through the circuit.
(Self) Inductance: (Self) Inductance refers to the property of a single coil or circuit that causes it to oppose changes in current flowing through it, measured by its self-inductance coefficient, $L$.