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  4. 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 L, total number of turns N and radius r is less than (πμ0N2r2/L) Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current I is B=(μ 0NI/L) in the middle of the solenoid but becomes less as we move towards its ends.

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Q. 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 $L$, total number of turns N and radius r is less than $\frac{\pi\mu_{0}N^{2}r^{2}}{L}$
Statement 2: The magnetic induction in the solenoid in Statement 1 carrying current $I$ is $B=\frac{\mu _{0}NI}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.

AIEEEAIEEE 2012Electromagnetic Induction

Solution:

Self inductance of a long solenoid is given by
$L=\frac{\mu_{0}N^{2}A}{l}$
Magnetic field at the centre of solenoid
$B=\frac{\mu _{0}NI}{l}$
So both the statements are correct and statement 2 is correct explanation of statement 1