Q. A physicist works in a laboratory where the magnetic field is $2T$. She wears a necklace enclosing area $0.01m^{2}$ in such a way that the plane of the necklace is normal to the field and is having a resistance $R = 0.01\ \Omega$. Because of power failure, the field decays to 1$T$ in time $10^{- 3}seconds$. Then what is the total heat produced in her necklace? $(T = tesla)$
A) $10\ J$
B) $20\ J$
C) $30\ J$
D) $40\ J$
Explanation
(a) $H = \frac{V^{2}t}{R}$ and $V = \frac{N\left( B_{2} - B_{1} \right)A\cos\theta}{t}$
$V = \frac{1 \times (1 - 2) \times 0.01 \times \cos{0{^\circ}}}{10^{- 3}} = 10\ V$
So, $H = \frac{(10)^{2} \times 10^{- 3}}{0.01} = 10\ J$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.