14.1 Mutual Inductance

A current $I \left(t\right) = \left(5.0 \text{A}\right) \text{sin} \left(\left(120 \pi \text{rad}/\text{s}\right) t\right)$ flows through the solenoid of part (b) of the example. What is the maximum emf induced in the surrounding coil?

Show that $N \Phi_{\text{m}} / I$ and $\epsilon / \left(d I / d t\right) ,$ which are both expressions for self-inductance, have the same units.

The ignition circuit of an automobile is powered by a 12-V battery. How are we able to generate large voltages with this power source?

An emf of $9.7 \times 10^{−3} \text{V}$ is induced in a coil while the current in a nearby coil is decreasing at a rate of 2.7 A/s. What is the mutual inductance of the two coils?

A coil of 40 turns is wrapped around a long solenoid of cross-sectional area $7.5 \times 10^{−3} \text{m}^{2} .$ The solenoid is 0.50 m long and has 500 turns. (a) What is the mutual inductance of this system? (b) The outer coil is replaced by a coil of 40 turns whose radius is three times that of the solenoid. What is the mutual inductance of this configuration?

A toroidal coil has a mean radius of 16 cm and a cross-sectional area of $\left(0.25 \text{cm}\right)^{2}$; it is wound uniformly with 1000 turns. A second toroidal coil of 750 turns is wound uniformly over the first coil. Ignoring the variation of the magnetic field within a toroid, determine the mutual inductance of the two coils.