Question

A square loop of side 20 cm is initially kept 30 cm away from a region of uniform magnetic filed of 0.1 T as shown in the figure. It is then moved towards the right with a velocity of $10cm{s}^{-1}$ till it goes out of the field. plot a graph showing the variation of
(i) magnetic flux $\left(\varphi \right)$ through the loop with time(t).
(ii) induced emf $\left(\epsilon \right)$ in the loop with time t.
(iii) induced current in the loop, if it has resistance of 0.1 $\Omega$.

Answer 1

From $t=0$ to $t=3s(=\frac{30cm}{10cm/sec})$ the flux through coil is zero.

From $t=3s$ to $t=5s$ the flux through coil increases from

$0to[0.1\times (\frac{20}{100}{)}^2]Wb$ i.e. $0.004Wb$

From $t=5s$ to $t=11s$ the flux remains constant at the value $0.004Wb$ .

From $t=11s$ to $t=13s$ the flux decreases and becomes zero.

(i) $E=-\frac{d\varphi }{dt}=\text{slope}=\frac{0.004}{2}=2\times {10}^{-3}V$

(ii) $i=\frac{E}{R}=\frac{2\times {10}^{-3}}{0.1}=20mH$