Question

A long solenoid is fabricated to closely winding wire of radius $0.5$mm over a cylinderical frame, so that the successive turns nearly touch each other. The magnetic field at the centre of solenoid, if it carries a current of $5$A is?

• A. $2\pi \times {10}^{-2}$T
• B. $2\pi \times {10}^{-3}$T
• C. $2\pi \times {10}^{-4}$T
• D. $2\pi \times {10}^{-5}$T

Answer 1

The correct option is B $2\pi \times {10}^{-3}$T

The turns of wire on the solenoid are shown in figure.
Number of turns in $1$mm $=1$
$n=1000$turns$/$m
$\therefore B={\mu }_{0}ni$
$=4\pi \times {10}^{-7}\times {10}^3\times 5$
$=2\pi \times {10}^{-3}$T.