Q 12-06-121JEE MainJEE Main 2020 (8 Jan, Shift 1)Medium
At time $t = 0$, a magnetic field of $1000$ gauss is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500$ gauss in the next $5$ s, then the induced EMF in the loop is:
Answer: (A) $56\ \mu\text{V}$
Area of the loop: the $16\ \text{cm}\times4$ cm rectangle minus two triangular notches, each of base $4$ cm and height $2$ cm:
$$A = 64 - 2\times\frac12\times4\times2 = 56\ \text{cm}^2 = 56\times10^{-4}\ \text{m}^2$$
Rate of change of field: $\dfrac{(1000 - 500)\times10^{-4}\ \text{T}}{5\ \text{s}} = 10^{-2}$ T/s.
$$\varepsilon = A\frac{dB}{dt} = 56\times10^{-4}\times10^{-2} = 56\ \mu\text{V}$$
Solution by Sreeraj P, M.Sc Physics