A wire carrying a current of 6 A is bent into a circular arc of radius 2 cm . If the arc subtends an angle of 120^ at the centre of curvature, the magnitude of the magnetic field at the centre is: (Take permeability of free space as 4 10⁻⁷ T m A ⁻¹ )

Step-by-step solution

The magnetic field at the centre of a circular arc subtending an angle is given by a fraction of the field of a complete circular loop: B = ( 360^ ) ₀ I 2R Given: = 120^ I = 6 A R = 2 cm = 0.02 m Substituting the values: B = ( 120^ 360^ ) 4 10⁻⁷ 6 2 0.02 B = ( 1 3 ) 24 10⁻⁷ 0.04 B = 8 10⁻⁷ 0.04 B = 200 10⁻⁷ T B = 20 10⁻⁶ T = 20 T Answer: 20 T