Question

The diagram shows a circuit that is laid out in the shape of a square that is 2 m on a side. The circuit consists of a constant source of EMF and three series resistors. Voltmeters are used to determine the potential difference of all four of the circuit elements. These potential differences are shown in the diagram.
Which of the following can explain why the sum of the potential differences does not equal zero?

• A. This situation is impossible because it violates Kirchhoff's Loop Rule.
• B. This situation is possible if a constant magnetic field of strength 40 T passes through the square circuit.
• C. This situation is possible if a constant magnetic field of strength 10 T passes through the square circuit.
• D. This situation is possible if a magnetic field changing at a rate of 40 T/s passes through the square circuit.
• E. This situation is possible if a magnetic field changing at a rate of 10 T/s passes through the square circuit.

Answer 1

The correct option is E This situation is possible if a magnetic field changing at a rate of 10 T/s passes through the square circuit.

The above situation can be possible only if some emf is induced in the square circuit due to change in magnetic flux crossing the loop.

Magnitude of required induced emf $E=100-10-20-30=40$ V

Let magnetic field changing with time passes through the circuit.

Area of the circuit $A=2^2=4$ $m^2$

$\therefore$ $E=\frac{d\left(BA\right)}{dt}=A\frac{dB}{dt}$

OR $40=4\times \frac{dB}{dt}$ $⟹\frac{dB}{dt}=10$ T/s

Thus the above situation is possible if a magnetic field changing at a rate of 10 T/s passes through the square circuit.