Question

A closely wound solenoid $80cm$ long has $5$ layers of winding of $400$ turns each. The diameter of the solenoid is $1.8cm$. If the current carried is $8.0A$, 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
$B={\mu }_{0}nI$
Here, ${\mu }_0=4\pi \times 10^{-7}Tm{A}^{-1}$
$n=$ Number of turns per unit length of the solenoid
$=\frac{\text{ Total number of turns }}{\text{ Length of the solenoid }}$
$=\frac{5\times 400}{80\times 10^{-2}}{m}^{-1}$
$I=8.0A$ (Given)
$\therefore B=4\pi \times 10^{-7}\times \frac{5\times 400}{80\times 10^{-2}}\times 8$
$=8\pi \times 10^{-3}T$