Question

A solenoid of $2.5 \, m$ length and $2.0 \, cm$ diameter possesses $10$ turns per cm. A current of $0.5 \, A$ 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
$\because \, \, \frac{\mu _{0}}{4 \pi }=10^{- 7}TA^{- 1}$
$\Rightarrow \, \, \mu _{0}=4\pi \times 10^{- 7}TA^{- 1} \, $
Given, $n=10 \, cm^{- 1}=1000 \, m^{- 1}$
$I=0.5 \, A$
$\therefore \, \, B=4\pi \times 10^{- 7}\times 1000\times 0.5$
$=2\pi \times 10^{- 4}T$