Q. 495.0( 1 Vote )

# A long, cylindrical wire of radius b carries a current i distributed uniformly over its cross section. Find the magnitude of the magnetic field at a point inside the wire at a distance a from the axis.

Answer :

Given:

Radius of wire = b

Current distributed throughout the cross section = i

Diagram:

Formula used:

Ampere’s circuital law states that the line integral of the magnetic field for a closed surface is μ0 times the current enclosed by the surface.

, where B = magnetic field, dl = line element, μ0 = magnetic permeability of vacuum, I = current enclosed.

Since the current i is uniformly distributed throughout the cross section of the wire,

For an amperian loop of radius a(a<b) from the center of the wire,

I (current enclosed)

Where

i= total current distributed throughout the wire,

b = radius of the wire,

a = distance from the axis at which the magnetic field is to be found.

Hence, from Ampere’s circuital law,

since 2πa = circumference of Amperian loop of radius a, and I = enclosed current = ia2/b2.

Therefore, magnetic field at a distance a from the axis inside the wire,

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