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JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2025 · 29 January · Morning Shift · Physics · Electromagnetic Induction

A coil of area A and N turns is rotating with angular velocity (ω)...

A coil of area A and N turns is rotating with angular velocity (\omega) in a uniform magnetic field (\vec{B}) about an axis perpendicular to (\vec{B}). Magnetic flux (\varphi) and induced (\operatorname{emf} \varepsilon) across it, at an instant when (\vec{B}) is parallel to the plane of coil, are :A coil of area A and N turns is rotating with angular velocity (ω) in a uniform magnetic field ( B ) about an axis

Options

  1. A(\varphi=\mathrm{AB}, \varepsilon=0)
  2. B(\varphi=0, \varepsilon=0)
  3. C(\varphi=0, \varepsilon=\mathrm{NAB} \omega)
  4. D(\varphi=\mathrm{AB}, \varepsilon=\mathrm{NAB} \omega)

Correct answer

C. (\varphi=0, \varepsilon=\mathrm{NAB} \omega)

Step-by-step solution

A coil of area A and N turns is rotating with angular velocity (ω) in a uniform magnetic field ( B ) about an axis
ϕ=BAN⋅cos⁡(ωt)ε=−dϕdt=BAω N⋅sin⁡(ωt)\begin{aligned} \phi & =\mathrm{BAN} \cdot \cos (\omega \mathrm{t}) \\ \varepsilon & =\frac{-\mathrm{d} \phi}{\mathrm{dt}}=\mathrm{BA} \omega \mathrm{~N} \cdot \sin (\omega \mathrm{t}) \end{aligned} When BB is parallel to plane, ωt‾‾=π2⇒ϕ=0,ε=BAω N\underline{\underline{\omega t}}=\frac{\pi}{2} \Rightarrow \phi=0, \varepsilon=\mathrm{BA} \omega \mathrm{~N}
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