Two Conducting Plates
a cross section of a thin infinite conducting plate with excess positive charge we know that this excess charge lies on the surface of the plate Since the plate is thin and very large we can assume that essentially all the excess charge is on the two large faces of the plate If there is no external electric field to force the positive charge into some particular distribution it will spread out on the two faces with a uniform surface charge density of magnitude we know that just outside the plate this charge sets up an electric field of magnitude E = er[ /eo. Because the excess charge is positive, the field is directed away from the plate shows an identical plate with excess negative charge having the same magnitude of surface charge density The only difference is that now the electric field is directed toward the plate Suppose we arrange for the plates of and b to be close to each
other and parallel Since the plates are conductors when we bring them
into this arrangement the excess charge on one plate attracts the excess charge on the other plate and all the excess charge moves onto the inner faces of the plates as in With twice as much charge how on each inner face, the new surface charge density (call it er) on each inner face is twice er the electric field at any point between the plates has the magnitude
This field is directed away from the positively charged plate and toward the negatively charged plate. Since no excess charge is left on the outer ‘£aces, the electric field to the left and right of the plates is zero Because the charges on the plates moved when we brought the plates close to each other the superposition of and b that is the charge distribution of t e two-plate system is not merely the sum of the charge distributions of the individual plates.You may wonder why we discuss such seemingly unrealistic situations as the field set up by an infinite line of charge, an infinite sheet of charge or a pair of infinite plates of charge One reason is that analyzing such situations with Gauss’ law is easy. More important is that analyses for “infinite” situations yield good approximations to many real-world problems Thus holds well for a finite nonconducting sheet as long as we are dealing with points close to the sheet and not too near its edges holds well for a pair of finite conducting plates as long as we consider points that are not too close to their edges.The trouble with the edges of a sheet or a plate. and the reason we take care not to deal with them is that near an edge we can no longer use planar symmetry to find expressions for the fields.In fact the field lines there are curved (said to be an edge effect or fringing), and the fields can be very difficult to express algebraically.