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JEE Main 20203 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
3 September
Shift
Evening Shift
Subject
Physics
Chapter
Electromagnetic Induction

JEE Main 2020 · 3 September · Evening Shift · Physics · Electromagnetic Induction

A uniform magnetic field B exists in a direction perpendicular to...

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4mm4mm and a total length of 30cm.30cm . The magnetic field changes with time at a steady rate dB/dt=0.032Ts−1.dB / dt = 0 . 032{Ts}^{- 1} . The induced current in the looploopis close to (Resistivity of the metal wire is 1.23×10−8Ωm1 . 23 \times {10}^{- 8}Ωm )A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The

Options

  1. A0.43 A
  2. B0.61 A
  3. C0.34 A
  4. D0.53 A

Correct answer

B. 0.61 A

Step-by-step solution

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The

Radius =d/2=2mm= d / 2 = 2mm

Rwire=ρlA{R}_{wire} = \dfrac{ρl}{A}

ϕ=BA;∣e∣=dϕdt=dBdt(A)ϕ = BA; \left|e\right| = \dfrac{dϕ}{dt} = \dfrac{dB}{dt}\left(A\right)

i=eR=∣dBdt∣(A)2ρl=0.032×{π×2×10−3}21.23×10−8×4×0.3i = \dfrac{e}{R} = \left|\dfrac{dB}{dt}\right|\dfrac{{\left(A\right)}^{2}}{ρl} = \dfrac{0 . 032 \times {\left\{\pi \times 2 \times {10}^{- 3}\right\}}^{2}}{1 . 23 \times {10}^{- 8} \times 4 \times 0 . 3}

=0.61A= 0 . 61A

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