Electromagnetic Induction and Alternating Current 3 Question 3

3. 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/L

(b) L2

(c) L

(d) 1/L2

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Answer:

Correct Answer: 3. (a)

Solution:

  1. (a) Self inductance Lsol of a solenoid is given by

Lsol=μ0n2πr2L

(Here, n=N/L and L= length of solenoid)

 or Lsol=μ0N2πr2L Clearly, Lsol1L

( All other parameters are fixed)

NOTE We can determine expression of L as follows

φ=NBA=Lsol l

But for a solenoid, B=μ0nl,A=π2

Lsol l=μ0n/π2N or Lsol =μ0n2π2L=μ0N2Lπr2



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