CBSE Class 12 · 2005 · All India · Electromagnetic InductionShort Answer

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Define self-inductance and give its S.I. unit. Derive an expression for the self-inductance of a long, air-cored solenoid of length

ℓ

, radius

r

, and having

N

number of turns.

Solution

Definition: the self-inductance of a coil equals the flux linkage set up per unit current flowing through it; its S.I. unit is the henry (H).
For a long solenoid of

N

turns, length

ℓ

and cross-section

A = π r^{2}

carrying current

I

, the interior field is

B = μ_{0} \frac{N}{ℓ} I

Flux through one turn is

B A

, so the total flux linkage is

N ϕ = N (B A) = \frac{μ _{0} N ^{2} I A}{ℓ}

Since

N ϕ = L I

L = \frac{μ _{0} N ^{2} A}{ℓ} = μ_{0} n^{2} A ℓ

where

n = N / ℓ

is the number of turns per unit length.

CBSE Class 12 Board · 2005 · All India · Subjective

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