A circular wire loop of radius $50 \mathrm{mm}$ carries a current of $80 \mathrm{A}$. Find the (a) magnetic field induction, and (b) energy density at the centre of the loop. 

In given figure, two straight conducting rails form a right angle. A conducting bar in contact with the rails starts at the vertex at time $t=0$ and moves with a constant velocity of $8.90 \mathrm{m} {\mathrm{s}}^{-1}$ along them. A magnetic field with $B=0.350 \mathrm{T}$ is directed out of the page. Calculate $\left(\mathrm{a}\right)$ the flux through the triangle formed by the rails and bar at $t=3.00 \mathrm{s}$and $\left(\mathrm{b}\right)$ the emf around the triangle at that time.$\left(c\right)$ If the emf is $\epsilon =a{t}^n,$ where $a$ and $n$ are constants, what is the value of $n ?$ 

A solenoid having an inductance of $9.70 \mu \mathrm{H}$ is connected in series with a $1.20 \mathrm{k\Omega }$ resistor.

$\text{(a)}$ If a $14.0 \mathrm{V}$ battery is connected across the pair, how long will it take for the current through the resistor to reach $40.0\%$ of its final value?
$\left(b\right)$ What is the current through the resistor at time $t=0.50 {\tau }_L$? 

In the given figure, a wire loop of lengths $L=50.0 \mathrm{cm}$ and $W=20.0 \mathrm{cm}$ lies in a magnetic field $\overrightarrow{B}$. What are the
$\left(\mathrm{a}\right)$ Magnitude of induced EMF $\epsilon$ and $\left(b\right)$ direction (clockwise or counterclockwise or none if $\epsilon =0$) of the emf induced in the loop, if $\overrightarrow{B}=\left(4.00\times {10}^{-2} \mathrm{T} {\mathrm{m}}^{-1 }\right)y \hat{\mathrm{k}}$ ? What are $\left(\mathrm{c}\right)$ $\epsilon$ and $\left(\mathrm{d}\right)$ the direction, if $\overrightarrow{B}=\left(6.00\times {10}^{-2} \mathrm{T} {\mathrm{s}}^{-1}\right)t \hat{\mathrm{k}}?$ What are $\left(e\right)$$\epsilon$ and $\left(f\right)$  the direction, if $\overrightarrow{B}=\left(8.00\times {10}^{-2} \mathrm{T} {\mathrm{m}}^{-1} {\mathrm{s}}^{-1}\right)yt \hat{\mathrm{k}}$ ? What are $\left(g\right) \epsilon$ and $\left(\mathrm{h}\right)$ the direction, if $\overrightarrow{B}=\left(3.00\times {10}^{-2}\mathrm{T} {\mathrm{m}}^{-1} {\mathrm{s}}^{-1}\right)xt \hat{\mathrm{j}}$? What are $\left(i\right)$ $\epsilon$ and $\left(j\right)$ the direction, if $\overrightarrow{B}=\left(5.00\times {10}^{-2} \mathrm{T} {\mathrm{m}}^{-1} {\mathrm{s}}^{-1})\right.$$yt \hat{\mathrm{i}}$?  

Figure (a) shows a circuit consisting of an ideal battery with emf $\epsilon =6.00 \mathrm{\mu V}$, a resistance $R,$ and a small wire loop of area $5.0 {\mathrm{cm}}^2$. For the time interval $t=10 \mathrm{s}$ to $t=20 \mathrm{s}$, an external magnetic field is set up throughout the loop. The field is uniform, its direction is into the page in Figure (a) and the field magnitude is given by $B=at$, where $B$ is in $\mathrm{tesla}$, $a$ is a constant and $t$ is in seconds. Figure (b) gives the current $i$ in the circuit before, during and after the external field is set up. The vertical axis scale is set by $i_{\mathrm{s}}=4.0 \mathrm{mA}$. Find the constant $a$ in the equation for the field magnitude. 

$\left(\mathrm{a}\right)$  $\left(\mathrm{b}\right)$