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QJEEM23Ph498d: JEE Main 2023 Physics - Class 12 JEEM23Ph498d Solution: The magnetic field B crossing normally a square metallic plate…

The magnetic field B crossing normally a square metallic plate of area 4 m24 \mathrm{~m}^{2} is changing with time as shown in figure. The magnitude of induced emf in the plate during t=2s\mathrm{t}=2 s to t=4s\mathrm{t}=4 s , is __________ mV\mathrm{mV} .

JEE Main 2023 (Online) 11th April Morning Shift Physics - Electromagnetic Induction Question 32 English

Step-by-Step Verified Solution

amp;m=tan⁡θ=105=2amp; B=mtamp;B=2t\begin{aligned}& \mathrm{m}=\tan \theta=\frac{10}{5}=2 \\\\& \mathrm{~B}=\mathrm{mt} \\\\& \mathrm{B}=2 \mathrm{t}\end{aligned}

amp;ε=∣dϕdt∣=d(BA)dt=AdBdtamp;ε=4 d(2t)dt=4×2=8mV\begin{aligned}& \varepsilon=\left|\frac{\mathrm{d} \phi}{\mathrm{dt}}\right|=\frac{\mathrm{d}(\mathrm{BA})}{\mathrm{dt}}=\frac{\mathrm{AdB}}{\mathrm{dt}} \\\\& \varepsilon=\frac{4 \mathrm{~d}(2 \mathrm{t})}{\mathrm{dt}}=4 \times 2=8 \mathrm{mV}\end{aligned}

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