An infinite plane slab of thickness 2d extends from y=−d to y=+d along the y-axis and is infinite in the x- and z-directions. Throughout the region −d<y<0 it carries a uniform current density J=Jz^, while in the region 0<y<d it carries an equal current density in the opposite direction, J=−Jz^.
a. (i) Derive an expression for the magnetic field B(y) for all points inside the slab (∣y∣<d).
b. (ii) Obtain B(y) for regions outside the slab (∣y∣>d).
c. (iii) Sketch the variation of the magnitude of B with y from y=−2d to y=+2d and indicate clearly the direction of the field in each region.