The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

Question

The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to : (A) 1/L2 (B) 1/L (C) L (D) L2

Tardigrade Admin · Accepted Answer

Φ = NBA = LI N μ0 nI π R2 LI N μ0 (N/ℓ) I π R2 = LI N R constant self inductance (L) propto (1/ℓ) propto (1/length) Option (2)

Q. The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

1/L²

1/L

L

L²

$Φ = NB A = L I$
$N μ_{0} n I π R^{2} L I$
$N μ_{0} \frac{N}{ℓ} I π R^{2} = L I$
N & R constant
self inductance (L) \propto $\frac{1}{ℓ}$ \propto $\frac{1}{l e n g t h}$
Option (2)

Q. The total number of turns and cross-section area in a solenoid is fixed. However, its length L is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to :

1/L2

1/L

L

L2

Φ=NBA=LI Nμ0​nIπR2LI Nμ0​ℓN​IπR2=LI N & R constant self inductance (L) \propto ℓ1​ \propto length1​ Option (2)

1/L²

L²

$Φ = NB A = L I$
$N μ_{0} n I π R^{2} L I$
$N μ_{0} \frac{N}{ℓ} I π R^{2} = L I$
N & R constant
self inductance (L) \propto $\frac{1}{ℓ}$ \propto $\frac{1}{l e n g t h}$
Option (2)