Question

In the following situations, determine the magnetic induction,magnetic field,magnetization, and bound current inside qnd outside the magnetic bodies.

a.A magnetic wire with a uniform free current density along its length

b. An infinite magnetic slab with a sheet current at its center

Answer 1

a)Let R be the radius of the wire and I be the free current through the wire

Using amperes law,

Inside the wire, considering a loop of radius s

where is the unit vector along direction in cylindrical coordinate system.

Outside the wire,

Outside the wire magetization M=0 (Because no materia outside the wire)

So magetic field

Inside the wire, Magnetic field is,

Bound current

Outside the wire since M=0

Inside the wire,

b)In part b question is not clear.

But here I am assuming that the current is uniform throughout the width of the wire.

Then outside the slab, considering a loop of width l such that the current flows parallel to the area normal vector of the loop. (Assume current is flowing into the plane of the screen. Then the loop lies on the screen)

Then using the amperes law, only the sides of the loop parallel to the sheet contributes to the integral because the contribution of perpendicular sides is zero due to the dot product in amperes law.

Then,

where J(Amp/m^2) is the surface charge density, d is the thickness of the slab.

Inside the wire, consider a loop of width x and length y. Then

Direction will be to the left above the slab and to the right below the slab.

If the current is not uniform througout the width of the slab, instead a sheet of current, then H inside and outside the slab will be the same.

Similar to case a, M outside the slab will be zero.