Alpha Geek
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1. a) Show that ?? ?t + ? · j = 0 is the mathematical expression of charge conservation. b) In a conducting medium j = sE, where s is the conductivity of the medium (which is constant) and E is the electric field. (This is just another way of writing Ohm’s law.) Insert this relation into the continuity equation and see what conclusions you arrive at. 2. a) An infinite plane carries charge s per unit area. Determine its electric field. b) Suppose that the plane has a straight, very narrow, infinitely-long gap of width d. What is the electric field at a distance D directly above the gap, for D d? 3. a) Consider two inertial frames S and S 0 , the latter moving with velocity v with respect to the former along their common z axis. Transform ? · B = 0 from one frame to the other and see what you conclusions you can draw. b) If magnetic charge existed, we would have ? · B = µo ?m, where ?m is the density of magnetic charge. How would the existence of magnetic charge affect the rest of Maxwell equations? What physical phenomena would be associated with the existence of magnetic charge?