A circular coil has $15.0 \mathrm{cm}$ radius and consists of $30.0$ closely wound turns of wire. An externally produced magnetic field of magnitude $2.60 \mathrm{mT}$ is perpendicular to the coil. (a) If no current is in the coil, what magnetic flux links its turns?
(b) When the current in the coil is $2.80 \mathrm{A}$ in a certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil?

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?

In the figure (a), a uniform magnetic field $\overrightarrow{B}$ increases in magnitude with time $t$ as given by the figure (b) where the vertical axis scale is set by $B_{\mathrm{s}}=9.0 \mathrm{mT}$ and the horizontal scale is set by $t_{\mathrm{s}}=3.0 \mathrm{s}$. A circular conducting loop of area $8.0\times {10}^{-4} {\mathrm{m}}^2$ lies in the field in the plane of the page. The amount of charge $q$ passing point $A$ on the loop is given in the figure (c) as a function of $t$, with the vertical axis scale set by $q_{\mathrm{s}}=$$12 \mathrm{mC}$ and the horizontal axis scale again set by $t_{\mathrm{s}}=1.5 \mathrm{s}$. What is the loop's resistance?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

$\left(\mathrm{c}\right)$ 

In figure, a $120$ turn coil of radius $1.8 \mathrm{cm}$ and resistance $5.3 \mathrm{\Omega }$ is coaxial with a solenoid of $220$ $\mathrm{turns} {\mathrm{cm}}^{-1}$ and the diameter $3.2 \mathrm{cm}$. The solenoid current drops from $0.42 \mathrm{A}$ to zero in time interval $\Delta t=0.67 \mathrm{s}$ What current is induced in the coil during $\Delta t$?