Question

A solenoid of $2.5m$ length and $2.0cm$ diameter possesses $10$ turns per cm. A current of $0.5A$ is flowing through it. The magnetic induction at axis inside the solenoid is

• A. $2\pi \times 10^{-4}T$
• B. $2\pi \times 10^{-5}T$
• C. $2\pi \times 10^{-6}T$
• D. $2\pi \times 10^{-7}T$

Answer 1

Answer: (A)

The magnetic induction along the axis of solenoid
$B={\mu }_{o}nI$
Where, $n=$ number of turns per unit length
and $I=$ current
$\because \frac{{\mu }_0}{4\pi }=10^{-7}T{A}^{-1}$
$\Rightarrow {\mu }_0=4\pi \times 10^{-7}T{A}^{-1}$
Given, $n=10c{m}^{-1}=1000m^{-1}$
$I=0.5A$
$\therefore B=4\pi \times 10^{-7}\times 1000\times 0.5$
$=2\pi \times 10^{-4}T$