Electromagnetic Induction

JEE Main level, single correct, medium

139 of 153

Question 139 of 153

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement 1: Self inductance of a long solenoid of length
LL, total number of turns N\mathrm{N} and radius r\mathrm{r} is less than πμ0N2r2L\frac{\pi \mu_0 N^2 r^2}{L}.
Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current
II is μ0NIL\frac{\mu_0 N I}{L} in the middle of the solenoid but becomes less as we move towards its ends.

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Answer: (B) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.

Self inductance of a long solenoid is given by
L=μ0N2AlL=\frac{\mu_0 N^2 A}{l}
Magnetic field at the centre of solenoid

B=μ0NIlB=\frac{\mu_0 N I}{l}
So both the statements are correct and statement 2 is correct explanation of statement 1

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