7.3 Two point charges and a plane Please include a picture and be specific with

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7.3 Two point charges and a plane

Please include a picture and be specific with your steps. PLEASE use good handwriting. About half of the time I get answers I cannot tell what symbols are being used and the answer becomes worthless to me. Explain what the symbol means if possible. Thanks!

7.3 Two point charges and a plane Two point charges qi and q2 are located near a grounded conducting plane that is infinite in extent. a) Find the values and locations of the image charges that are needed to make the plane a surface of constant potential b) Confirm that the values and locations of the image charges that you obtained in part (a) give an electrostatic potential 1-0 everywhere on the grounded conducting plane. c) From the result of part (a), predict the image-charge distribution required for a charged body of arbitrary shape and charge density (7) that is situated near a conducting plane of infinite extent.

Explanation / Answer

given, for two point charges q1 and q2 located near a grounded conductor that is infinite in extent

a. the values and locations of the image charges required to make the plane surface a constant potential surface are as under

place a mirror in place of the plane and find the mirror images of the charges

the charges are -q1 and -q2

the locations are on the opposite side of the plane with same respective perpendicular distance from the plane as that of original charges ( like mirror images from mirrors)

as this configuration will always have same potential 0 V for all distances from the charges hence this configuration will work

b. now distance of the grounded plane from q1 and -q1 is same for all points on plane hence contribution of these two in potential is 0. same is the case with the q2 and -q2. hence this constant potential on the plane is 0 V

c. for any arbitraty body of charge density rho(r), we will need a body of charge densoty -rho(r) on the opposite side of the plane at tha same perpendicular distance from the plane to get 0V potential on the plane

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