Question

The magnetic field in the cylindrical region shown in the figure. increase at a constant rate of 20.0 mT/s. Each side of the square loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 $\mho$. Find the current (magnitude and sense) in the wire and if
(a) the switch $S_1$ is closed but $S_2$ is open,
(b) $S_1$ is open but $S_2$ is closed,
(c) both $S_1$ and $S_2$ are open and
(d) both $S_1$ and $S_2$ are closed.

Answer 1

(a) $S_{1}closed,S_{2}open$

$e=\frac{d\varphi }{dt}=A\frac{dB}{dt}{10}^{-4}\times 2\times {10}^{-6}$

$=2\times {10}^{-6}$

current through ad

$i=\frac{e}{r}$ = $\frac{2\times {10}^{-6}}{16}=1.25\times {10}^{-7}A$ along ad.

(b) $R=16\Omega$

$e=A\times A\times \frac{dB}{dt}=2\times {10}^{-5}v$

$i=\frac{2\times {10}^{-6}}{16}=.25\times {10}^{-7}A$

(c) Since both S1 and S2 are open No current is passed as a circuit is open that is i = o

(d) since both S1 and S2 are closed the circuit from a balanced wheatstone bridge and no current wire flow along and that is i = 0