A piece of wire carrying a current of 6.00 A is bent in the form of a circular arc of radius 10.0 cm, and it subtends an angle of 120° at the center. Find the magnetic field B due to this piece of wire at the center.
Given:
Radius of circular arc(r) = 10 cm = 0.1 m
Current carried by it(i) = 6 A
Angle subtended at the center = 1200
Formula used:
Magnetic field at the center of a circular arc,
Where
μ0 = magnetic permeability of vacuum = 4π x 10-7 kg m s-2 A-2,
i = current carried by the wire,
r = radius of the wire,
θ = angle subtended at the center of the arc
Diagram:
Hence, required magnetic field
where, i = 6 A, r = 0.1 m, θ = 1200 = 2π/3 radian, μ0 = 4π x 10-7 kg m s-2 A-2
Hence, B = 
= 1.256 x 10-5 T = 12.56 μT (Ans)
1