5. Equipotential spheres. Two point charges +q and -q are placed on the x-axis a

Question

5. Equipotential spheres. Two point charges +q and -q are placed on the x-axis as shown in the figure below. Show that the equipotential surfaces (the dashed lines) are spheres of increasing radii that surround each respective charge, and are offset from the charges themselves. (In the lab we did on electric charge, those conductive spheres acted as equipotential surfaces; that is, one set of dashed lines here in the figure would represent a charged sphere. In this system, the entire distribution of charge can be represented by just these two charges, q and -q, at the indicated positions.) Hint: Pick a point P with coordinates (x.y). Draw straight lines from q and -q, respectively. to that point. In terms of 'x', 'y', and a', write expressions that give the distances from q to P and from -q to P, respectively. Now, write an expression that gives the sum of the electric potentials due to each charge at point P. Let this sum be a constant, labeled Vo. Using algebra, manipulate the expression until it gives the equation of an offset circle, The constants ‘c, and 'R, will be expressions themselves, in terms of k, q, a, and Vo. -q +q x-axis

Explanation / Answer

These links will be helpful

http://arxiv.org/pdf/1211.4622.pdf

services.eng.uts.edu.au/pmcl/pct/Downloads/Lecture05.pdf

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