Name: Electric Field: Time Varying Magnetic Field
Uploaded: 2019-07-19
Duration: 8 min 32 s
Description: Did you know that the cause of the movement of charges in a stationary circular conducting coil placed in a time-varying magnetic field is due to an induced...

Question

Define self inductance. Write the SI unit. Find an expression for the self inductance of a coil. Give two factors on which self inductance of an air-cored coil depends.

Accepted Answer

Self inductance of a coil is equal to the e.m.f. induced in the coil when rate of change of current through the coil is unity.

The SI unit of self inductance is henry $(H)$ .

Mathematically,

Magnetic flux changes in the coil is directly proportional to the induced current produced in the coil.

$ϕ \propto I . . . (1) ϕ = L I . . . . . (2)$

Where, $L$ is a proportionality constant which is called self inductance.

$L = \frac{ϕ}{I} . . . . (3)$

If we take,

$I = 1 A . . . . (4) L = ϕ . . . . . (5)$

Self Inductance of a single coil is numerically equal to flux changes in the coil, provided induced current provided in the coil is $1$ Ampere.

Using Faraday Second law,

$e = - \frac{d ϕ}{d t} . . . . (6)$

Using equation $(2),$

$\Rightarrow e = \frac{- d}{d t} [L I] \Rightarrow e = - L \frac{d I}{d t} \Rightarrow L = \frac{e}{|- \frac{d I}{d t}|} . . . (7)$

$\Rightarrow \frac{- d I}{d t} = 1 A S^{- 1} \Rightarrow L = e$

Then, self inductance of a simple coil is numerically equal to induced emf produced in the coil provided change of induced current with respect to time is $1 A S^{- 1} .$

Self-inductance of the coil depends on the area of cross-section of the coil, the number of turns per unit length in the coil, the length of the solenoid and the permeability of the core material.

Define self inductance. Write the SI unit. Find an expression for the self inductance of a coil. Give two factors on which self inductance of an air-cored coil depends.

Important Questions on Electromagnetic Induction

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