Q. 45.0( 1 Vote )

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

B. minimum at the axis of the wire

C. maximum at the surface of the wire

D. minimum at the surface of the wire.


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.

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