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Question

Two solenoids of equal number of turns having their length and the radii in the same ratio 1:2. The ratio of their self-inductance will be

A
1:2
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B
2:1
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C
1:1
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D
1:4
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Solution

The correct option is A 1:2
Self inductance of a solenoid,
L=μ0N2Al=μ0N2πr2l
where l is the length of the solenoid, N is the total number of turns of the solenoid and A is the area of cross-section of the solenoid.
L1L2=(N1N2)2(r1r2)2(l2l1)
Here, N1=N2,l1l2=12,r1r2=12
L1L2=(12)2(21)=12


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