Q. A circuit area is $0.01\ m^{2}$ is kept inside a magnetic field which is normal to its plane. The magnetic field changes from 2 T to 1 T in 1 millisecond. If the resistance of the circuit is $2\Omega$. The amount of heat evolved is
A) 0.05 J
B) 50 J
C) 0.50 J
D) 500 J
Explanation
(a) Induced emf produced in coil
$e = \frac{- d\phi}{dt} = \frac{- d}{dt}(BA)$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ |e| = A\frac{dB}{dt} = 0.01 \times \frac{1}{1 \times 10^{- 3}}$
$|e| = 10\ V$
Current produced in coil,
$i = \frac{|e|}{R} = \frac{10}{2} = 5\ A$
Heat evolved $= i^{2}Rt$
$= (5)^{2} \times (2) \times 1 \times 10^{- 3} = 0.05\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.