Question

(a) State Ampere's circuital law, expressing it in the integral form.
(b) Two long coaxial insulated solenoids, $S_1$ and $S_2$ of equal lengths are wound one over the other. A steady current "I" flow through the inner solenoid $S_1$ to the other end B, which is connected to the outer solenoid $S_2$ through which the same current "I" flows in the opposite direction so as to come out at end A. If $n_1$ and $n_2$ 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 states that the circulation of the resultant magnetic field along a closed, plane curve is equal to ${\mu }_o$ times the total current crossing the area bounded by the curve.

$\overrightarrow{B}.\overrightarrow{dl}={\mu }_o{I}_{enclosed}$

(b)

(i) Inside a solenoid, magnetic field is given by ${\mu }_{o}ni$

In the given scenario, $B={\mu }_{o}I(n_1-n_2)$ as the currents are in the opposite direction. Direction of magnetic field is parallel to the axis of the solenoid and depends on the sign of $n_1-n_2$.

(ii) Outside a solenoid, magnetic field is zero.