MHTCET 13 Apr 2026 Shift 2 Paper

Concept:According to Faraday's law of electromagnetic induction, the induced emf in a loop equals the rate of change of magnetic flux linked with it.Explanation:The magnetic field is perpendicular to the plane of the loop, so the magnetic flux is $\Phi = BA$.From Faraday's law, the induced emf is $\varepsilon = \left|\frac{d\Phi}{dt}\right| = A\left|\frac{dB}{dt}\right|$.The radius of the circular loop is $r = \frac{10}{\sqrt{\pi}} \text{ cm}$.Therefore, its area is $A = \pi r^2 = \pi \left(\frac{10}{\sqrt{\pi}}\right)^2 = 100 \text{ cm}^2$.Converting to SI units: $A = 100 \times 10^{-4} = 10^{-2} \text{ m}^2$.The field decreases steadily from $0.5 \, \text{T}$ to zero in $0.5 \, \text{s}$, so the rate of change of the field is $\left|\frac{dB}{dt}\right| = \frac{0.5}{0.5} = 1 \, \text{T s}^{-1}$.Thus, the induced emf is $\varepsilon = 10^{-2} \times 1 = 10^{-2} \, \text{V} = 10 \, \text{mV}$.Since the field decreases at a steady rate, the induced emf remains constant at every instant, including $t = 0.25 \, \text{s}$.Answer:The induced emf at $0.25 \, \text{s}$ is $10 \, \text{mV}$, which is Option B.