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Electromagnetic Induction

Inductance

Have you seen a motor working? And do you know how does it work? Well, it works because of ‘inductance’. But actually what it means? Let us find out!

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Inductance

It is the current production in a coil due to change in magnetic flux in itself or new coil. Whenever there is a coil, and you have a change in magnetic flux or change in magnetic field, an induced emf is generated in that coil or wire. This very property is inductance.

Here Φ ∝ I, where, Φ is the magnetic flux and I is the current. In ‘n’ turns of the coil, N Φ ∝ I. It is a scalar quantity and it’s SI unit is Henry. It is denoted by H.

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Dependency of Geometric Parameters on Inductance of a Coil

  • The number of wire wraps or turns in the coil:  When there are a greater number of turns of wire in the coil it will result in greater inductance. And vice versa.
  • Coil area:  If the coil area is more, the coil (as measured looking lengthwise through the coil, at the cross-section of the core) results in greater inductance and vice versa.
  • Coil length: The longer the length of the coil, the inductance will be less. If the length of the coil the is shorter, the inductance will be greater.

Self Inductance

Self-induction means the coils induce the emf themselves. There is a change in the magnetic flux through that coil and because of this, the current will be induced in the coil by itself. So once the current get induced, the current tries to oppose the flux. Here NΦ ∝ I

NΦ = LI ( L is the self-induction)

Induced emf,  E = -N \( \frac{dΦ}{(dt)} \) =  -N \( \frac{dI}{(dt)} \) [ L/N]

E = -L \( \frac{dI}{(dt)} \)

This is the self-induced emf. A coil having self-inductance ”L” is said to be the induction coil.

Mutual Inductance

Here, there are two coils placed near each other. The first coil will make turns and carry the current which results in the magnetic field. As both the coils nearly close to each other, the magnetic field through one coil will all pass through the other coil.  So one coil causes the change in magnetic flux because of which current is induced in the other coil.

Here there is the primary coil and another one is the secondary coil. This type of induction mainly depends upon the number of turns, size, and shape of the coil and medium between the two coils.

E = -M \( \frac{dI}{(dt)} \)

Questions For You

Q1. What do we call the phenomenon of production of back emf in a coil due to the flow of varying current through it?

  1. Self-inductance
  2. Electromagnetic Induction
  3. Magnetic flux
  4. Magnetic moment

Answer: A. Self-inductance is that phenomenon in which charge in electric current in a coil produces an induced emf in the coil itself.

Q2. Two coils A and B have L= 2×10-2  Henry. If the current in the primary is i = 5 sin 10πθ  then maximum value of emf induced in coil B is:

  1. Π volt
  2. \( \frac{Π}{2} \) volt
  3. \( \frac{Π}{3} \) volt
  4. \( \frac{Π}{4} \) volt

Answer: A. Given that, Current i = 5sin (10πt), Mutual inductance L = 2×10-2 and H =0.02H

Induced emf, E = -M \( \frac{di}{dt} \)

∴ |E| = M × 5 (10π) cos (10πt)

= π volt

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