This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the…
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 $\mathrm{N}$ and radius $\mathrm{r}$ 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 $\frac{\mu_0 N I}{L}$ in the middle of the solenoid but becomes less as we move towards its ends.
Statement 1 is true, Statement 2 is false.
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
Statement 1 is false, Statement 2 is true.
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
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 N I}{l}
$
So both the statements are correct and statement 2 is correct explanation of statement 1