Problem

Sketch the equipotential lines a long distance fr…

Problem 38 Hard Difficulty

Figure 19.34 shows the electric field lines near two charges $q_{1}$ and $q_{2},$ the first having a magnitude four times that of the second. Sketch the equipotential lines for these two charges, and indicate the equipotential lines for these potential.

Answer

We first draw the electric field for the given charge distribution. The equipotential lines are drawn perpendicular to the electric field lines. The sketch of the equipotential lines near the two charges is shown in Figure $1 .$ Since $q_{1}$ is more negative than $q_{2},$ the electric field lines that begin on $q_{2}$ end on $q_{1}$ . Hence, the direction of increasing potential will be from $q_{1}$ to $q_{2}$ .

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Physics 102 Electricity and Magnetism

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Chapter 19

Electric Potential and Electric Field

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Video Transcript

So let him force drop how the lines are drawn in figure 1934. So Lyons looks somewhat like this. Oh, sorry for that. So these lines are not affected. Similarly, there are lions here which are not drawn in the diagram. So let me draw one more line. So since the charge, cute too is positive, or at least from the diagram, it looks positive because all the lions are originating from que tu and ending up on the Cuban so lip. So let me draw arrows on all of these lines. So when you draw equal potential surface, all you have to do is to draw a perpendicular from this light on this lines. So see that you can draw, uh, a surface which are of pending killer, which is perpendicular to this. These electric field lights. So this is you're but every potential surface. I think the surface similarly, there will be a potential surface on this side. So all you have to maintain is these lines include potential surface are perpendicular to the the electric field lights, so you can see that the distance here is smaller than distance on this side. That happens because in the mid in between the plus Q and Cuban and cute. Oh, that is plus Cuban negative. Thank you. The potential new too negative. Three cues negative and potentially to positive. Q is positive so they can sell out. Can send some of the part, not completely, and there is somewhere between them. You'll find the surface goes somewhat like this. So this surface has which is which is a bit closer to kill and then so cute to than Cuban Mrs Q. To here. And this is Cuban here because Cuban is three times large or four times larger in magnitude. Yes, it's four times larger than the man in the magnitude. So this is closer Cuban, where the potential is you. So below that or outside of this surface, you can see that the potential surfaces are at far distance on the right inside to look you two on closer as I am drawing here on inside. Same is the fact for Cuban

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