Question

A piece of wire carrying a current of 6.00 A is bent in the form of a circular are of radius 10.0 cm, and it subtends an angle of 120° at the centre. Find the magnetic field B due to this piece of wire at the centre.

Answer 1

Given:
Magnitude of current, I = 6 A
Radius of the semi-circular wire, r = 10 cm
Angle subtended at the centre, θ = 120° = $\frac{2\mathrm{\pi }}{3}$
∴ Required magnetic field at the centre of curvature
$$\begin{gathered} B=\frac{{\mathrm{\mu }}_{0}i}{2r}\frac{\theta }{2\mathrm{\pi }} \\ =\frac{4\times {10}^{-7}\times 5}{2\times 10\times {10}^{-2}}\times \frac{2\mathrm{\pi }}{3\times 2\mathrm{\pi }} \\ =4\mathrm{\pi }\times {10}^{-6} \\ =1.26\times {10}^{-5}\mathrm{T} \end{gathered}$$