I E Irodov Solutions for Chapter: ELECTRODYNAMICS, Exercise 6: ELECTROMAGNETIC INDUCTION. MAXWELL'S EQUATIONS

A closed circuit consists of a source of constant emf $\xi$ and a choke coil of inductance $L$, connected in series. The active resistance of the whole circuit is equal to $R$. At the moment $t=0$, the choke coil inductance was decreased abruptly, $\eta$ times. Find the current in the circuit as a function of time $t$.

Instruction: During a stepwise change of inductance, the total magnetic flux (flux linkage) remains constant.

Find the time dependence of the current flowing through the inductance $L$, of the circuit shown in the figure, after the switch $Sw$ is shorted at the moment $t=0$.

In the circuit shown in the figure, an emf $\xi$, a resistance $R$ and coil inductance $L_1$ and $L_2$, are known. The internal resistance of the source and the coil resistances are negligible. Find the steady state currents in the coils, after the switch $Sw$ was shorted.

Calculate the mutual inductance of a long straight wire and a rectangular frame with sides $a$ and $b$. The frame and the wire lie in the same plane, with the side $b$ being closest to the wire, separated by a distance $I$ from it, and oriented parallel to it.

Determine the mutual inductance of a doughnut coil and an infinite straight wire passing along its axis. The coil has a rectangular cross-section, it's inside radius is equal to $a$, and the outside one, to $b$. The length of the doughnut's cross-sectional side, parallel to the wire, is equal to $h$. The coil has $N$ turns. The system is located in a uniform magnetic field with permeability $\mu$.

Two thin concentric wires shaped as circles with radii $a$ and $b$ lie in the same plane. Allowing for $a\ll b,$ find,
(a) their mutual inductance,
(b) the magnetic flux through the surface enclosed by the outside wire, when the inside wire carries a current $I$.

There are two stationary loops with mutual inductance $L_{12}$. The current in one of the loops starts to be varied as $I_1=\alpha t$, where $\alpha$ is a constant, $t$ is time. Find the time dependence $I_2\left(t\right)$ of the current in the other loop, whose inductance is $L_2$ and resistance is $R$.

A coil of inductance $L=2.0 \mathrm{\mu H}$ and resistance $R=1.0 \mathrm{\Omega }$, is connected to a source of constant emf $\xi =3.0 \mathrm{V}$. A resistance $R_0=2.0 \mathrm{\Omega }$, is connected in parallel with the coil. Find the amount of heat generated in the coil, after the switch $Sw$ is disconnected. The internal resistance of the source is negligible.