Question

A solenoid is $2.0$ m long and $3.0$ cm in diameter. It has $5$ layers of winding of $1000$ turns each and carries a current of $5.0$ A. What is the magnetic field at its centre?

• A. $1.5\times {10}^{-3}T$
• B. $1.5\times {10}^{-2}T$
• C. $1.5\times {10}^{-4}T$
• D. $2.5\times {10}^{-2}T$

Answer 1

The correct option is B $1.5\times {10}^{-2}T$

Here total number of turns
$N=5\times 1000=5000$
Length of the solenoid $l=2.0m$
$\therefore$ Number of turns per unit length
$n=\frac{N}{l}=\frac{5000}{2}=2500$
current $I=5.0A,{\mu }_0=4\pi \times {10}^{-7}H{m}^{-1}$
$B={\mu }_{0}nI=4\pi \times {10}^{-7}\times 2500\times 5$
$=1.5\times {10}^{-2}T$