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Question

A long solenoid of N turns has a self inductance L and area of cross section A. When a current i flows through the solenoid, the magnetic field inside it has magnitude B. The current i is equal to:

A
BNAL
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B
BANL
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C
BNAL
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D
BANL
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Solution

The correct option is A BNAL
Number of turns of solenoid =N

Number of turns per unit length is,

n=Nl

Where, l is the length of the solenoid.

Magnetic field inside the solenoid is,

B=μ0ni

B=μ0Nil ...(1)

Also, self inductance of solenoid is,

L=μ0n2Al

L=μ0(Nl)2×Al

L=μ0N2Al ...(2)

From equations (1) and (2),

BL=iNA

i=BNAL

​​​​​​​Hence, (A) is the correct answer.

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