Question:

A 800 turn coil of effective area 0.05 $m^2$ is kept perpendicular to a magnetic field $5\times 10^{-5}$ T. When the plane of the coil is rotated by $90^\circ$ around any of its coplanar axis in 0.1 s, the emf induced in the coil will be

Updated On: May 17, 2024
  • $2\times 10^3$V
  • 0.02 V
  • 2V
  • 0.2 V
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The Correct Option is B

Solution and Explanation

Magnetic field $B = 5 \times 10^{-5} \; T$
Number of turns in coil N = 800
Area of coil A = 0.05 $m^2$
Time taken to rotate $\Delta$t = 0.1 s
Initial angle $\theta_1 = 0^{\circ}$
Final angle $\theta_2 = 90^{\circ}$
Change in magnetic flux $\Delta \phi$
$ = NBA \cos 90^{\circ} - BA \cos 0^{\circ}$
= - NBA
$ = - 800 \times 5 \times 10^{-5} \times 0.05$
= - 2 $\times 10^{-3} $ weder
$e =- \frac{\Delta\phi}{\Delta t} = \frac{-\left(-\right)2\times10^{-3}Wb}{0.1 s} = 0.02 V $
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Top Questions on Electromagnetic induction

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Concepts Used:

Electromagnetic Induction

Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-

  1. When we place the conductor in a changing magnetic field.
  2. When the conductor constantly moves in a stationary field.

Formula:

The electromagnetic induction is mathematically represented as:-

e=N × d∅.dt

Where

  • e = induced voltage
  • N = number of turns in the coil
  • Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
  • t = time

Applications of Electromagnetic Induction

  1. Electromagnetic induction in AC generator
  2. Electrical Transformers
  3. Magnetic Flow Meter