A piece of wire bent into a weirdly shaped loop, as shown in the diagram, carries a current that increases linearly with time:
Since V=0 we have just
ANSWER: Finding requires knowledge of the dependence of on ; but we have calculated only at one point in space! If you want a differentiable you will have a far more difficult calculation to perform.
ANSWER: Suppose the field point is a perpendicular distance s from the string; measure z from the nearest point on the string, as shown in the diagram. Equation (10.68), in which we do not need to evaluate anything at a retarded time, gives the contribution to from a single charge q. We need to superimpose such contributions from all charge elements at positions down the string: for each of these we use :