Question

A long solenoid is fabricated by closely winding a wire of radius 0.5 mm over a cylindrical nonmagnetic frame so that the successive turns nearly touch each other. What would be the magnetic field B at the centre of the solenoid if it carries a current of 5 A?

Answer 1

Given:
Radius of the wire, r = 0.5 mm
Width of each turn, = diameter of the wire, 2r = 1 mm = 1 × 10⁻³ m
∴ Total number of turns in 1 m solenoid
$$\begin{gathered} n=\frac{1}{1\times {10}^{-3}}={10}^3 \\ \mathrm{Magnitude}\mathrm{of}\mathrm{current},\mathit{}i=5\mathrm{A} \\ \mathrm{Using}B={\mathrm{\mu }}_{0}ni,\mathrm{we}\mathrm{get} \\ B=4\mathrm{\pi }\times {10}^{-7}\times {10}^3\times 5 \\ B=2\mathrm{\pi }\times {10}^{-3}\mathrm{T} \end{gathered}$$