Question

Question 1: Find the potential of an electric dipole at a point P some radius away by superposing the point charge potentials of the two charges. A diagram of the setup is shown below: +q -q Question 2: I'd like to use the answer to Question 1 to find the capacitance between two spheres of opposite charge distance d apart, with some fixed radii R, but I won't necessarily get the right answer, write why not. Estimate the required relationship between d and R to only get a 10% error.

Answer 1

As we know that V = kq{1/r - d/2 cos theta - 1/r + d/2 cos theta = kq d cos theta/r^2 - f^2/4 cos^2 theta r_+ = r - d/2 cos theta r - = r + d/2 cos theta for r > > d v = kqd cos theta/r^2 = kp cos theta/r^2 {k = 1/4 pi elementof_0 p = qd v = 1/4 pi elementof_0 p cos theta/r^2 As we know that E = theta/4 pi elementof_0 r^2 integral dv = integral E dr = theta/4 pi elementof_0 integral dr/r^2 delta v = theta/4 pi elementof_0[- 1/r]^R + d_R delta v = theta/4 pi elementof_0 {1/R - 1/R + d} Hence c = theta/v = 4 pi elementof_0/[1/R - 1/R + d]