Q85 / 90 · JEE Main 2024 (05 Apr Shift 2) · Physics
A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $\mathrm{m}$ ' number of turns. It carries a current of $5 \mathrm{~A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$ then the value of $m$ is _____.
Correct answer: 500
Solution
$\mu_0 n i=B \quad n=$ number of turns per unit length
$\mu_0\left(\frac{\mathrm{m}}{\ell}\right) \mathrm{i}=\mathrm{B}$
$\begin{aligned} & \mathrm{m}=\frac{B . \ell}{\mu_0 \mathrm{i}}=\frac{6.28 \times 10^{-3} \times 0.5}{12.56 \times 10^{-7} \times 5} \\ & \mathrm{~m}=500\end{aligned}$
Hence, the correct answer is 500.