Question

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.

• A. Statement 1 is true, Statement 2 is false
• B. Statement 1 is true, Statement 2 is true. Statement 2 is the correct explanation of Statement 1
• C. Statement 1 is false, Statement 2 is true
• D. Statement 1 is true, Statement 2 is true. Statement 2 is not the correct explanation of Statement 1

Answer 1

Answer: (B)

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