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Two Point Charges
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Two point charges q1. =- q and q2 = +įq are placed at the origin and at the 9 point (a,0,0) respectively. a) At what point xo along the x axis does the electric field vanish? Begin with a one-dimensional drawing of the charges along the x axis. Number these regions as follows: Region I: x<0, Region II: 0<x<a, and Region III: x > a. Draw the fields due to each of the point charges in each of the three regions, and decide which region could have a vanishing field before deriving the spe- cific point. Make sure that your result lies in the appropriate region. b) Draw a 3D picture with the charges on the x axis, and draw a position vec- tor ř = xî + yỹ + zł. Also draw the vectors from each of the charges to the point † and label them appropriately. Then write down the general electrostatic potential 0(x, y, z) in Cartesian coordinates for the two point charges. Use this to show that the Ø(x, y, z) = 0 equipotential surface is spherical in shape. [You will have to complete the square to show that the equation you get is that for a sphere.] c) Find the radius and the coordinates of the center of the spherical equipoten- tial surface of part (b).