Question

(a) State Ampere's circuital law, expressing it in the integral form.
(b) Two long coaxial insulated solenoids, S₁ and S₂ of equal lengths are wound one over the other as shown in the figure. A steady current "I" flow thought the inner solenoid S₁ to the other end B, which is connected to the outer solenoid S₂ through which the same current "I" flows in the opposite direction so as to come out at end A. If n₁ and n₂ are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside on the axis and (ii) outside the combined system.

Answer 1

(a) Ampere’s circuital law : The line integral of the magnetic field around a closed path is times of total current enclosed by the path.

Expression of the law in integral form :

(b) (i)

Magnitude of net magnetic field inside the combined system on the axis,

Also accept if the student writes

(ii) Outside the combined system, the net magnetic field is zero.