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So let's go back to our dipole for a second. And we know what a dipole looks like it's a positive charge and then a negative charge. And now we know what the electric field looks like for a dipole. It goes like this. and you'll see these sorts of pictures again and again particularly in your chemistry books. So this is the lines of E for the dipole. What about equipotential surfaces? Well, We said that the equipotential surfaces always have to be perpendicular to E. So if there is some equipotential surface right here it has to start out perpendicular to that line. But the next one's a little curved so I gotta make sure I'm perpendicular to that line and then the next one is at a different angle and then the next one is at a different angle and so forth and if I do a curve like that I am perpendicular to the lines of E everywhere. All right. But by symmetry I can do on the other side, right, it'll look nearly the same. That's an equipotential surface for the negative charge. but likewise I can come right across the center here. That's an equipotential surface. And you can keep going you can draw as many as you like That's gonna be one that looks like this there's going to be one that looks like this and so forth. Okay these are all equipotential surfaces these dashed lines. Now what's sort of interesting about an equipotential surface is since it's perpendicular to V particles can move along those lines without having any work done on them. Because remember in our work equation it was FD cosine theta and if theta is 90 degrees, the cosine of 90 degrees is of course zero. So a charge can move along one of these lines without having any work done on it at all. Okay let's try an example of calculating the potential for a slightly more complicated arrangement of charges.

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