Answer to Question #74008 in Electricity and Magnetism for tal

Question

1 A square loop of edge L located in the xy plane at z = 0 carriesa clockwise current i as indicated on the right.
a) Show that, for rp = zp^z on the axis of the loop at a distance zp from its center,
H(z) =4iL2/pi*(4z^2 + L^2)*(4z2 + 2L2)^0.5

3. A long cylindrical non-magnetic conductor of radius R0; whose axis coincides
with the ^z-axis, carries a uniformly distributed current I0 in the +^z direction. A cylindrical
hole is now drilled out of the conductor, parallel to the axis, so that the cross section is shown
below. The centre of the hole is at x = a, and the radius is b.
Determine the magnetic eld ~H inside the hole.
4. A horizontal strip of negligible thickness, made of non-magnetic material, having width d and extending from y = -d/2 to y = d/2 in the y-direction, and innitely long in the x-direction, is placed in the xy plane. Find H at rp = (0; 0; z0) if

a) the strip has a surface current density ~Ks = K0^x,
b) the strip has a surface current density ~Ks = K0