Electric Field and Potential of Symmetric Charges · CAP 2010 #Q14

Physics · electromagnetism

Problem

Eight identical negative charges -q are arranged symmetrically on a circle of radius r, each equidistant from the next. Assume the point charges have zero potential at infinity. If the constant of proportionality in Coulomb's law is k, then the magnitude of the electric field and the electrostatic potential at the centre of the circle are given by a) E=8kqr2,V=−8kqrE= \frac{8kq}{r²}, V = \frac{-8kq}{r}; b) E=8kq(2πr)2,V=−8kq(2πr)E = \frac{8kq}{(2πr)²}, V = \frac{-8kq}{(2πr)}; c) E=8kqr2,V=0E= \frac{8kq}{r²}, V =0; d) E=0,V=0E =0,V =0; e) E=0,V=−8kqrE =0, V = \frac{-8kq}{r}. [Figure: Eight negative charges arranged symmetrically on a circle]

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