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?

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?

Toppr Admin · Accepted Answer

The turns of wire on the solenoid are shown in figure-Number of turns in 1mm -1n-1000turns-m-x2234-B-x3BC-0ni-4-x3C0-xD7-10-x2212-7-xD7-103-xD7-5-2-x3C0-xD7-10-x2212-3T-

A long solenoid is fabricated to closely winding wire of radius 0.5mm 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 5A is?2π×10−2T2π×10−3T2π×10−4T2π×10−5T

The turns of wire on the solenoid are shown in figure.Number of turns in 1mm =1n=1000turns/m∴B=μ0ni=4π×10−7×103×5=2π×10−3T.

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