Show that in an ideal toroid, the magnetic field inside the toroid at any point in the open space is zero.

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.

A long straight wire of a circular cross-section of radius $\text{'}a\text{'}$ carries a steady current $\text{'}I\text{'}$. The current is uniformly distributed across the cross-section. Apply Ampere's circuital law to calculate the magnetic field at a point $\text{'}r\text{'}$ in the region for $r<a$.

A long straight wire of a circular cross-section of radius $\text{'}a\text{'}$ carries a steady current $\text{'}I\text{'}$. The current is uniformly distributed across the cross-section. Apply Ampere's circuital law to calculate the magnetic field at a point $\text{'}r\text{'}$ in the region for $r>a$.