(a) Ampere's circuital law states that the circulation of the resultant magnetic field along a closed, plane curve is equal to $\mu_0$ times the total current crossing the area bounded by the closed curve, provided the electric field inside the loop remains constant. In the above illustration, the Ampere's circuital law can be written as follows: $\oint \vec{B} \cdot d\vec{l} = \mu_0 i$ $\; \text{ where } \; i = i_1 - i_2$ (b) (i) The magnetic field due to a current carrying solenoid: $B = \mu_0 n i$ where, $n=$ number of turns per unit length, $i=$ current through the solenoid. Now, the magnetic field due to solenoid $S_1$ will be in the upward direction and the magnetic field due to $S_2$ will be in the downward direction (by righthand screw rule).$B \; \text{ net } \; \; = B_1 - B_2$$\; = \mu_0 n_1 I - \mu_0 n_2 I$$\; = \mu_0 I (n_1 - n_2)$(ii) The magnetic field is zero outside a solenoid.