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Question

Area of a long solenoid is doubled.So how many times we have to increase its length to keep its self inductance constant-

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 2
N=total number of turns in solenoid
l=length of solenoid
R=radius of cross section of solenoid
Magnetic field inside solenoid =B=μoNli where, Nl=number of turns per unit length

Now, emf induced= E=NBA

E=N×μoNli×A

E=μoN2Ali=Li
where L=self inductance
L=μoN2Al

LAl

The length of solenoid should be doubled also on doubling the area to keep L constant.

Answer-(B)

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