Q. 425.0( 2 Votes )

# 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.

Answer :

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

μ_{0} = 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 = 120^{0} = 2π/3 radian, μ_{0} = 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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