Now suppose that we had two curved plastic rods, one of charge + Q and the other

Question

Now suppose that we had two curved plastic rods, one of charge + Q and the other of charge -2Q, that form a whole circle of radius R in the x-y plane as shown below. Again, let's consider that each rod has its own uniform charge distribution. How could we quickly determine the electric field be at the center of the circle using the work that we did earlier? Which of the semi-circular rods below with the given uniformly distributed charge would produce the same electric field at its center as the configuration above?

Explanation / Answer

11) its very simple all we need to knw is the centroind of a half ring, which is ewual to 2pi/r from the cenytre of the big ring so assume the total charge concentrated at 2pi/r on both above and below the centroid as as we did earlier the net field can be determined when two points are acting charges 12) 1st figure as the charge can be assumed to be Q on top and -Q and -Q on bottom side one Q from top and one -Q from bottom will result in no electric field therefore the net field will be resulting inly from the remaining one -Q charge on bottom hence the choice

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