In figure (a) a circular loop of wire is concentric with a solenoid and lies in a plane perpendicular to the solenoid's central axis. The loop has radius $6.00 \mathrm{cm}$ The solenoid has radius $2.00$ $\mathrm{cm}$, consists of $5000 \mathrm{turns} {\mathrm{m}}^{-1}$ and has a current $i_{\text{sol }}$ varying with time $t$ as given in figure (b) where the vertical axis scale is set by $i_{\mathrm{s}}=1.00 \mathrm{A}$ and the horizontal axis scale is set by $t_{\mathrm{s}}=2.0 \mathrm{s}$ figure (c) shows, as a function of time, the energy $E_{\text{th }}$ that is transferred to the thermal energy of the loop; the vertical axis scale is set by $E_{\mathrm{s}}=100.0 \mathrm{nJ}$ What is the loop's resistance?

$\left(\mathrm{a}\right)$ 

$\left(\mathrm{b}\right)$ 

$\left(\mathrm{c}\right)$ 

Figure shows, a rod of length $L=12.0 \mathrm{cm}$ that is forced to move at constant speed of $v=5.00 \mathrm{m} {\mathrm{s}}^{-1}$ along the horizontal rails. The rod, rails and connecting strip at the right form a conducting loop. The rod has resistance $0.400 \mathrm{\Omega }$ and the rest of the loop has negligible resistance. A current $i=100 \mathrm{A}$ through the long straight wire at distance $a=5.00$ $\mathrm{mm}$ from the loop sets up a (non-uniform) magnetic field through the loop. Find the
(a) emf and
(b) current induced in the loop. (c) At what rate is thermal energy generated in the rod? (d) What is the magnitude of the force that must be applied to the rod to make it move at constant speed?
(e) At what rate does this force do work on the rod?

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 $a.$