JEE PYQ: Electromagnetic Induction Question 8
Question 8 - 2020 (05 Sep Shift 1)
Two concentric circular coils, $C_1$ and $C_2$, are placed in the XY plane. $C_1$ has 500 turns, and a radius of 1 cm. $C_2$ has 200 turns and radius current 20 cm. $C_2$ carries a time dependent current $I(t) = (5t^2 - 2t + 3)$ A where $t$ is in s.
The emf induced in $C_1$ (in mV), at the instant $t = 1$ s is $\frac{4}{x}$. The value of $x$ is ____.
Show Answer
Answer: 5
Solution
$\phi_{\text{small}} = BA = \frac{\mu_0 N_2}{2R} \times (\pi r^2)$. Induced emf $e = \frac{\mu_0 N_1 N_2 \pi r^2}{2R} \frac{dI}{dt}$. At $t = 1$, $\frac{dI}{dt} = 10t - 2 = 8$. Computing: $e = \frac{4(4\pi)10^{-7} \times 200}{20} \times 500 \times \frac{10^{-4}}{10^{-2}} \times 8 = 8 \times 10^{-4}$ V $= 0.8$ mV $= \frac{4}{5}$ mV, so $x = 5$.
BETA
