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 centre.

Step-by-step solution

The magnetic field at the centre of a circular arc is given by: B = ₀ I 4 r Given: I = 6.00 A r = 10.0 cm = 0.1 m = 120^ = 2 3 rad Substituting the values: B = 4 10⁻⁷ 6.00 4 0.1 2 3 B = 10⁻⁶ 60 2 3 B = 40 10⁻⁷ T B = 4 3.14 10⁻⁶ T = 1.256 10⁻⁵ T 1.26 10⁻⁵ T