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

The correct option is A $2\pi \times {10}^{-4}T$

The magnetic induction along the axis of solenoid
$B={\mu }_{0}nI$
where, $n=$ number of turns per unit length
and $I=$ current
$\because \frac{{\mu }_0}{4\pi }={10}^{-7}T/A$
$\Rightarrow {\mu }_0=4\pi \times {10}^{-7}T/A$
Given : $n=10c{m}^{-1}=1000m^{-1}$
Current $I=0.5A$
$\therefore B=4\pi \times {10}^{-7}\times 1000\times 0.5$
$B=2\pi \times {10}^{-4}T$.