Question:

A coil having 500 square loops of side 10 cm is placed normal to magnetic field which increases at a rate of 1 T s$^{-1}$. The induced e.m.f. is

Updated On: Aug 26, 2023
  • 0.1 V
  • 0.5 V
  • 1 V
  • 5 V
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The Correct Option is D

Solution and Explanation

Here, area $A = 500 (10/100)^2 = 5\, m^2$
${ \frac{dB}{dt} = 1 \, T \, s^{-1}}$
Induced e.m.f $\left|e\right| =\frac{d\phi}{dt} =\frac{A dB}{dt} = 5\times 1 $ = 5 volt.
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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