Question:

A long solenoid has $1000$ turns. When a current of $4\,A$ flows through it, the magnetic flux linked with each turn of the solenoid is $4 \times 10^{-3} \, Wb$. The self-inductance of the solenoid is :

Updated On: May 21, 2024
  • 3 H
  • 2 H
  • 1 H
  • 4 H
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The Correct Option is C

Solution and Explanation

Flux linked with each turn $= 4 \times 10^{-3} \, Wb$
$\therefore$ Total flux linked = $ 1000[4 \times 10^{-3}] Wb$
$\phi_{total} = 4 \, \Rightarrow \, L \, i = 4 \, \Rightarrow \, L = 1 H $
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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