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 square loop abcd and defa has a length of 1.00 cm and a resistance of 4.00 Ω. Find the current (magnitude and sense) in the wire ad if (a) the switch S1 is closed but S2 is open, (b) S1 is open but S2 is closed, (c) both S1 and S2 are open and (d) both S1 and S2 are closed.
Figure

Answer 1

Use Wheat Stone Bridge

Explanation:

(a) $S_1$ closed $S_2$ open.

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

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

Current i through ad = $\frac {e}{R}$

= $\frac {2 \times 10^-^6}{16}$

= 1$0.25 \times 10^-^7$ A along ad  

b) R = $16 \Omega$

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

i = $\frac {2 \times 10^-^6}{16}$

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

c) Since both $S_1 and S_2$ are open, no current is passed as circuit is open i.e. i = 0  

(d) Since both $S_1 and S_2$2 are closed, the circuit forms a balanced wheat stone bridge and no current will flow along ad i.e. i = 0.