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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.
Options:
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.
Solution:
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Verified Answer
The correct answer is:
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
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
$$
L=\frac{\mu_0 N^2 A}{l}
$$
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
$$
L=\frac{\mu_0 N^2 A}{l}
$$
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
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