State Ampere's circuital law. Use this law to find magnetic field due to straight infinite current.

Two long coaxial insulated solenoids, $S_1$ and $S_2$ of equal lengths are wound one over the other, as shown in the figure. A steady current $"I"$" flows 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 inside on the axis.

Two long coaxial insulated solenoids, $S_1$ and $S_2$ of equal lengths are wound one over the other, as shown in the figure. A steady current $"I"$" flows 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 outside the combined system.