A piece of wire carrying a current of 6.00 A is shaped into a circular arc of radius 10.0 cm . If the arc subtends an angle of 120^ ^ ^ at the centre, determine the magnetic field B produced by this piece of wire at the

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Correct answer: B. 1.26 × 10^ -5 T

The magnetic field at the centre of a circular arc is given by:

B = \dfrac{\mu_0 I}{4\pi r} \theta

Given:

I = 6.00 \text{ A}

r = 10.0 \text{ cm} = 0.1 \text{ m}

\theta = 120^{}^{{}^{\circ}} = \dfrac{2\pi}{3} \text{ rad}

Substituting the values:

B = \dfrac{4\pi \times 10^{-7} \times 6.00}{4\pi \times 0.1} \times \dfrac{2\pi}{3}

B = 10^{-6} \times 60 \times \dfrac{2\pi}{3}

B = 40\pi \times 10^{-7} \text{ T}

B = 4 \times 3.14 \times 10^{-6} \text{ T} = 1.256 \times 10^{-5} \text{ T} \approx 1.26 \times 10^{-5} \text{ T}

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