PYQ NEET- Moving Charges And Magnetism L-2

Question: A long solenoid of radius $1 \mathrm{~mm}$ has 100 turns per $\mathrm{mm}$. If $1 \mathrm{~A}$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is#

A) $6.28 \times 10^{-2} \mathrm{~T}$

B) $12.56 \times 10^{-2} \mathrm{~T}$

C) $12.56 \times 10^{-4} \mathrm{~T}$

D) $6.28 \times 10^{-4} \mathrm{~T}$

Answer: (B) $12.56 \times 10^{-2} \mathrm{~T}$#

Sol:#

We know, magnetic field at centre of solenoid $$ \begin{aligned} & B=\mu_0 \frac{N}{l} l=\mu_0 n l\left[n=\frac{N}{l}\right] \ & =4 \pi \times 10^{-7} \times 100 \times 10^3 \times 1\left[n=\frac{100}{10^{-3}}\right] \ & =4 \pi \times 10^{-2} T \ & B=12.56 \times 10^{-2} T \end{aligned} $$