18.31.Set Up:For a point charge Solve: (a)and (c)The equipotential is the flat surface consisting of points equidistant from the two charges.The projection of this surface with a drawing in which the point charges are in the plane of the paper is a line alongthe perpendicular bisector of the line that connects the two charges, as shown in Figure 18.31.Figure 18.31(b)Since the point charges have equal magnitudes and opposite signs,at the point midway between them,since this point is equidistant from the two charges.18.32.Set Up:The electric field lines are perpendicular to the equipotential surfaces. The electric field lines arecloser together where Eis larger, and where Eis larger the equipotential surfaces for equal potential differences arecloser together. The projection of the equipotential surfaces into the plane of the figure are lines that satisfy these tworequirements.Solve:For the electric field given in the problem it is not possible to draw equipotential lines that satisfy bothrequirements. The electric field shown in the problem cannot be produced by an electrostatic distribution of charges.
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