A conducting wire is bent into a circular arc of radius 2 cm and subtends an angle of 60^ at its centre. If a steady current of 12 A is passed through the wire, what is the magnitude of the magnetic field produced at the centre of the arc? (Take the permeability of free space ₀ = 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The magnetic field at the centre of a circular arc is given by the formula: B = ₀ I 4 R Given: I = 12 A R = 2 cm = 2 10⁻² m = 60^ = 3 rad ₀ = 4 10⁻⁷ T m A ⁻¹ Substituting the values into the formula: B = 4 10⁻⁷ 12 4 2 10⁻² 3 B = 10⁻⁷ 12 2 10⁻² 3 B = 6 10⁻⁵ 3 B = 2 10⁻⁵ T B = 20 10⁻⁶ T = 20 T Answer: 20 T