Q 12-06-098JEE MainJEE Main 2022 (26 Jul, Shift 2)Medium
In a coil of resistance $8\ \Omega$, the magnetic flux due to an external magnetic field varies with time as $\phi = \dfrac23(9 - t^2)$. The value of total heat produced in the coil, till the flux becomes zero, will be ______ J.
Numerical value type. Enter your answer.
Answer: 2
$|\varepsilon| = \left|\dfrac{d\phi}{dt}\right| = \dfrac43t$. The flux becomes zero at $t = 3\ \text{s}$.
$$H = \int_0^3\frac{\varepsilon^2}{R}dt = \int_0^3\frac{16t^2}{9\times8}dt = \frac29\left[\frac{t^3}{3}\right]_0^3 = \frac29\times9 = 2\ \text{J}$$
Solution by Sreeraj P, M.Sc Physics