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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.
Solution
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
\[B = \frac{\mu_0 i}{2r}\frac{\theta}{2\pi}\]
\[ = \frac{4 \times {10}^{- 7} \times 5}{2 \times 10 \times {10}^{- 2}} \times \frac{2\pi}{3 \times 2\pi}\]
\[ = 4\pi \times {10}^{- 6} \]
\[ = 1 . 26 \times {10}^{- 5} T\]
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