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JEE Advanced 2025Paper 1
Exam
JEE Advanced
Year
2025
Paper
Paper 1
Subject
Physics
Chapter
Electromagnetic Induction

JEE Advanced 2025 · Paper 1 · Physics · Electromagnetic Induction

A conducting square loop initially lies in the X Z plane with its...

A conducting square loop initially lies in the XZX Z plane with its lower edge hinged along the XX-axis. Only in the region y≥0y \geq 0, there is a time dependent magnetic field pointing along the ZZ-direction, B⃗(t)=B0(cos⁡ωt)K^\vec{B}(t)=B_0(\cos \omega t) \hat{K}, where B0B_0 is a constant. The magnetic field is zero everywhere else. At time t=0t=0, the loop starts rotating with constant angular speed ω\omega about the XX axis in the clockwise direction as viewed from the +X+X axis (as shown in the figure). Ignoring self-inductance of the loop and gravity, which of the following plots correctly represents the induced e.m.f. ( VV ) in the loop as a function of time:
A conducting square loop initially lies in the X Z plane with its lower edge hinged along the X -axis. Only in the

Options

  1. A∫ ^ 4 x ^ 8 x dx is equal to (where C is an arbitrary constant)
  2. B∫ ^ 4 x ^ 8 x dx is equal to (where C is an arbitrary constant)
  3. C∫ ^ 4 x ^ 8 x dx is equal to (where C is an arbitrary constant)
  4. D∫ ^ 4 x ^ 8 x dx is equal to (where C is an arbitrary constant)

Correct answer

A. ∫ ^ 4 x ^ 8 x dx is equal to (where C is an arbitrary constant)

Step-by-step solution

ϕ=B0cos⁡ωtAsin⁡ωt=B0 Asin⁡2ωt2ε=−dϕdt=−B0 Acos⁡2ωt=(0≤t≤πω)ε=0(πω≤t≤2πω)\begin{aligned} & \phi=\mathrm{B}_0 \cos \omega \mathrm{tA} \sin \omega \mathrm{t}=\frac{\mathrm{B}_0 \mathrm{~A} \sin 2 \omega \mathrm{t}}{2} \\ & \varepsilon=-\frac{\mathrm{d} \phi}{\mathrm{dt}}=-\mathrm{B}_0 \mathrm{~A} \cos 2 \omega \mathrm{t}=\left(0 \leq \mathrm{t} \leq \frac{\pi}{\omega}\right) \\ & \varepsilon=0 \quad\left(\frac{\pi}{\omega} \leq \mathrm{t} \leq \frac{2 \pi}{\omega}\right)\end{aligned} Ans. Option (A)
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