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Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of 1 : 2.
The ratio of self-inductance of two solenoids is
  • a)
    1 : 1
  • b)
    1 : 2
  • c)
    2 : 1
  • d)
    1 : 4
Correct answer is option 'B'. Can you explain this answer?
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Two solenoids of same cross-sectional area have their lengths and numb...
Solution:

Given, two solenoids have their lengths and number of turns in the ratio of 1:2.

Let the first solenoid have length L and number of turns N.

Then, the second solenoid will have length 2L and number of turns 2N.

The self-inductance of a solenoid is given by,

L = μ₀n²Aℓ

where μ₀ is the permeability of free space, n is the number of turns per unit length, A is the cross-sectional area of the solenoid and ℓ is the length of the solenoid.

Let L₁ be the self-inductance of the first solenoid and L₂ be the self-inductance of the second solenoid.

Then,

L₁ = μ₀N²Aℓ

L₂ = μ₀(2N)²A(2L)

L₂ = 4μ₀N²A(2L)

L₂ = 8μ₀N²Aℓ

Therefore,

L₂/L₁ = 8μ₀N²Aℓ/μ₀N²Aℓ = 8/1

Hence, the ratio of self-inductance of the two solenoids is 1:2.

Therefore, option (b) is the correct answer.
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Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of 1 : 2.The ratio of self-inductance of two solenoids isa)1 : 1b)1 : 2c)2 : 1d)1 : 4Correct answer is option 'B'. Can you explain this answer?
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