# 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)

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