CBSE Class 12-science Answered

Since the current distribution possesses cylindrical symmetry, therefore the magnetic field it generates also possesses cylindrical symmetry. The magnetic field circulates in the x-y plane in an anti-clockwise direction.

 Let's first calculate the magnitude of magnetic field outside the wire and

apply Ampere's circuital law to a circular Amperian loop in the x-y plane where the loop is centered at the centre of the wire, and is of radius r>a, where “a” is the radius of the cylindrical wire.

As the magnetic field lines form closed circle, so the magnetic field is tangential to the loop everywhere, and is in the same direction as dl taken in the counter clock wise direction. Thus, the angle between the magnetic field and dl is zero everywhere on the loop.

Also, the magnitude of magnetic field is constant. So the situation is same as that for an infinitely thin wire.

From Ampere's law,

Since  is the circumference of the circle,

We have,  for r > a.          

Let us now apply Ampere's circuital law to a circular Amperian loop which is of radius r < a. The current I_e enclosed by the loop of radius r <a is

 From Ampere's law,