Consider two thin sheets at z = 0 and z = a, respectively, each with uniform sur

Question

Consider two thin sheets at z = 0 and z = a, respectively, each with uniform surface current density: K_0 hat x at z = 0, and -K_0 hat x at z = a. What is vector B between the two sheets, and also outside (above and below) both sheets. Does this remind you of a familiar electrostatics problem at all? How? Griffiths derives a formula for the vector B field from a solenoid (Example 5.9). Rewrite his answer (which is in terms of I) so it is expressed in terms of K (see his Figs. 5.34 and 5.35 for help with this). Can you comment on the similarity to the situation in part 3a?

Explanation / Answer

3a) For field at top and bottom,take  rectangular crosssection in yz plane such that one length y is just above the top plate, and other length is just below the bottom plate,

By amperes law,  B.dr = uo ienclosed

2By = uo*[K-K]y

B=0 at above and below

Magnetic field between the plate can be found be amperes law,

According to amperes law, B.dr = uo ienclosed

Take a rectangular crosssection in yz plane such that one length y is just above the top plate, and other length is just below the top plate

B.y= uo*Ky because at B at top is zero.

B = uoK in -y direction

similarly due to other plate also, B = uoK in -y direction;

net B = 2uoK in -y direction

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