At a given instant, the current and self-induced emf in an inductor are directed as indicated in the figure.
(a) Is the current increasing or decreasing?
(b) The induced emf is $23 \mathrm{V}$ and the rate of change of the current is $18 \mathrm{kA} {\mathrm{s}}^{-1}$ and find the inductance.

For the wire arrangement in the figure, $a=12.0 \mathrm{cm}$ and $b=16.0 \mathrm{cm}$.
The current in the long straight wire is $i=6.50t^2-10.0t$, where $i$ is in amperes and $t$ is in seconds. (a) Find the emf in the square loop at $t=3.00 \mathrm{s}$.
(b) What is the direction of the induced current in the loop?

A circular region in an $xy$ plane is penetrated by a uniform magnetic field in the positive direction of the $z$-axis. The fields magnitude $B$ (in $\mathrm{tesla}$) increases with time $t$ (in seconds) according to $B=at$, where $a$ is a constant. The magnitude $E$ of the electric field set up by that increase in the magnetic field is given by the figure versus radial distance $r$, the vertical axis scale is set by $E_{\mathrm{s}}=600 \mathrm{\mu N} {\mathrm{C}}^{\mathrm{-1}}\text{,}$ and the horizontal axis scale is set by $r_{\mathrm{s}}=4.00 \mathrm{cm}$. Find $a.$

The inductor arrangement of the figure with $L_1=50.0\mathrm{mH},$ $L_2=80.0\mathrm{mH}, L_3=20.0\mathrm{mH}$ and $L_4=15.0\mathrm{mH},$ is to be connected to a varying current source. What is the equivalent inductance of the arrangement?