Two very thin concentric hollow conducting cylinders with radii a and 3a carry uniformly distributed currents in opposite directions. The magnitude of the current through the inner cylinder with radius a is I, the magnitude of the current through the outer cylinder with radius 3a is 3/. Find the magnetic field at distance r from the axis of symmetry in the three regions (i) inside the inner cylinder (ii) between the two cylinders, and (iii) outside the outer cylinder. Show a sketch of the two cylinders which clearly indicates the direction of the currents as chosen by you. Also indicate the direction of the associated magnetic fields as you found for the three regions.

Two very thin concentric hollow conducting cylinders with radii a and 3a carry uniformly distributed currents in opposite directions. The magnitude of the current through the inner cylinder with radius a is I, the magnitude of the current through the outer cylinder with radius 3a is 3/. Find the magnetic field at distance r from the axis of symmetry in the three regions (i) inside the inner cylinder (ii) between the two cylinders, and (iii) outside the outer cylinder. Show a sketch of the two cylinders which clearly indicates the direction of the currents as chosen by you. Also indicate the direction of the associated magnetic fields as you found for the three regions.