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° = \[\frac{2\pi}{3}\]

∴ Required magnetic field at the centre of curvature

\[B =   \frac{\mu_0 i}{2r}\frac{\theta}{2\pi}\] 

\[ =   \frac{4 \times {10}^{- 7} \times 5}{2 \times 10 \times {10}^{- 2}} \times \frac{2\pi}{3 \times 2\pi}\] 

\[ =   4\pi \times  {10}^{- 6} \] 

\[ =   1 . 26 \times  {10}^{- 5}   T\]