Question

The magnetic field in the cylindrical region shown in figure increases at a constant rate of 20.0 mT/s. Each side of the wquare loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 $\Omega$. Find the current (magnitude and sense) in the wire ad 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) When $S_1$ closed and $S_2$ open

Net R = $4\times 4=16\Omega$

e = $\frac{d\Phi }{dt}=A.\frac{dB}{dt}$

= ${10}^{-4}\times 2\times {10}^{-2}$

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

Through ad = $\frac{e}{R}=\frac{2\times {10}^{-6}}{16}$

= $1.25\times {10}^{-7}$ A along ad.

(b) Here R = $16\Omega$

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

i = $\frac{20\times {10}^{-6}}{16}$

= $1.25\times {10}^{-7}$ A along da

(c) Since both $S_1$ and $S_2$ are open, no current is passed as circuit is open i.e.

i.e = 0

(d) Since both $S_1$ and $S_2$ are closed, the circuit forms a balanced wheatstone bridge and no current will flow along ad; i.e.

i = 0