Q74 / 90 · JEE Main 2012 (19 May Online) · Physics

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.

  • A
    Statement 1 is true, Statement 2 is false.
  • Correct answer
    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.

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

Hence, the correct answer is option: 'B'.

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