A long straight wire of radius R carries a current distributed uniformly over its cross section. The magnitude of the magnetic field is

Question

Philoid · Accepted Answer

According to Ampere’s Law:
Where,

dl is the current element,

B is the magnetic field,

μ₀ is the permeability of free space and

i is the current flowing.

Thus, at the cross-section the formula becomes,
2πR is the circumference of the wire and R is the radius. We get,
Now, at the axis of the wire. R=0, and so no area to integrate and hence zero current is enclosed. Thus magnitude of magnetic field is minimum at axis of the wire.
At the surface of the wire, R= some minimum value.
As R increases , magnitude of magnetic field decreases.
Hence, B will be maximum at the surface of the wire.
Thus, options (B) and (C) are correct options.