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4.
) Find the magnetic field of an infinite uniform surface current K = Kî,
flowing over the xy plane.

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Question A5 Consider an infinitely large sheet lying in the zz-plane at the origin, the extent of the sheet in the x, and z direction is infinite. The sheet carries surface current J = Jok, where Jo is the current per unit width perpendicular to the flow. Calculate the magnetic field everywhere (y > 0 and y < 0) due to J. Sketch the Amperian loop.
Problem 2 Show that in a current-free volume of space, a static magnetic field can never have a local maximum by considering V(B· B) · da, where S is the surface of a small volume V containing a point P in space.
A uniform magnetic field B has constant strength b teslas in the z-direction [i.e., B = (0, 0, b)] (a) Verify that A =Bxr is a vector potential for B, where r = (x, y, 0) (b) Calculate the flux of B through the rectangle with vertices A, B, C, and D in Figure 17. F B FIGURE 17 A = (8,0,4), B (8,5,0), C = (0,5,0), D = (0,0,4), F = (8,0,0) Flux(B) = -40b
3. A long cylindrical wire of radius R carrios a current I. The current density is non-uniform and can be expressed as J(r) = Jor? for 0 < r
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