1. Two infinite conducting planes at  z=0 and z=d carry currents in opposite directions with surface current density in the same  directions . Calculate the magnetic field everywhere in space.

Refer to the solution of Tutorial assignment 1. The field  due to a single plane carrying a linear current density is in direction  above the plane while below the plane it  is in direction.  Since the magnitude of the field is independent of distance, the field cancels between the planes and add up above the planes. For z > d, we have while for z<0 it is . Its value between the planes is zero.

2. Two infinite conducting sheets lying in x-z and y-z planes intersect at right angles along the z axis. On each plane a surface current . flows. Find the magnetic field in each of the four quadrants into which the space is divided by the planes.

Referring to the solution of tutorial problem 1, the field due to the current in xz plane is along above the plane (i.e. for and along below the plane (i.e. for

Likewise for the y-z plane, the field is along above the plane (i.e. for and along below( . The magnitude of the field in each case is the same and is . Thus the field along the first quadrant is and along the fourth is . One can similarly find the fields in the other two quadrants.

3. Consider the loop formed by two semicircular wires of radii and and two short straight sections, as shown. A current I flows through the wire. Find the field at the common  centre of the semicircles .

From  Tutorial problem 2 it follows that the contribution to the field due to two straight sections is zero.  The smaller semicircle  section gives a field  into the page while the bigger semicircle gives a field out of the page. The net field is (into the page)

4.The current density along a long cylindrical wire of radius a is given by , where r is the distance from the axis of the cylinder. Use Ampere’s law to find the magnetic field both inside and outside the cylinder.

First find the current enclosed within a distance r from the axis,

Thus the field inside is given by

Outside the cylinder the total current so that