Question

A closely wound solenoid $80 \,cm$ long has $5$ layers of winding of $400$ turns each. The diameter of the solenoid is $1.8\, cm$. If the current carried is $8.0\, A$, the magnitude of $B$ inside the solenoid near its centre will be

• A. $ 8\pi \times 10^{-3}\,T $
• B. $ 6\pi \times 10^{-3}\,T $
• C. $ 4\pi \times 10^{-3}\,T $
• D. $ 3\pi \times 10^{-3}\,T $

Answer 1

Answer: (A)

The magnitude of $\vec{B}$ inside the solenoid near its centre is
$B=\mu_{0} n I$
Here, $\mu_{0}=4 \pi \times 10^{-7}\, T\, m A^{-1}$
$n=$ Number of turns per unit length of the solenoid
$=\frac{\text { Total number of turns }}{\text { Length of the solenoid }}$
$=\frac{5 \times 400}{80 \times 10^{-2}} m^{-1}$
$I=8.0 \,A$ (Given)
$\therefore B=4 \pi \times 10^{-7} \times \frac{5 \times 400}{80 \times 10^{-2}} \times 8$
$=8 \pi \times 10^{-3}\, T$