PYQ NEET- Moving Charges And Magnetism L-4

Question: A long solenoid of $50 \mathrm{~cm}$ length having 100 turns carries a current of $2.5 \mathrm{~A}$. The magnetic field at the centre of the solenoid is : $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm}^{-1}\right)$#

A) $3.14 \times 10^{-4} T$

B) $6.28 \times 10^{-5} \mathrm{~T}$

C) $3.14 \times 10^{-5} \mathrm{~T}$

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

Answer: (D) $6.28 \times 10^{-4} \mathrm{~T}$#

Sol:#

Magnetic field at centre of solenoid $=\mu_0 n I$ $$ \begin{aligned} & n=\frac{N}{L}=\frac{100}{50 \times 10^{-2}} \ & =200 \text { turns } / \mathrm{m} \ & \text { । }=25 \mathrm{~A} \end{aligned} $$

Now, substituting the values, $$ \begin{aligned} & B=4 \pi \times 10^{-7} \times 200 \times 2.5 \ & =6.28 \times 10^{-4} \mathrm{~T} \end{aligned} $$