A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $m$ ' 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 :
JEE MAIN 2024, Diffcult
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$\mu_0 n i=B \quad n=$ number of turns per unit length
$\mu_0\left(\frac{\mathrm{m}}{\ell}\right) \mathrm{i}=\mathrm{B}$
$\mathrm{m}=\frac{\mathrm{B} \ell}{\mu_0 \mathrm{i}}=\frac{6.28 \times 10^{-3} \times 0.5}{12.56 \times 10^{-7} \times 5}$
$\mathrm{~m}=500$
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