The diagram shows the electric field around a charge. At which point on the diagram, 𝑃, 𝑅, or 𝑆, is the electric field strongest?
Looking at the diagram, we see this charge, the blue dot in the center, and the electric field lines pointing towards it. We also see the three points — point 𝑃, point 𝑅, and point 𝑆 — drawn in. The question is: at which of these three points is the electric field created by this charge, this blue dot, strongest? As we start out, notice that all of the arrows on the electric field lines point inward. That clues us in as to what the sign of this charge is.
If we were to sketch out the electric fields created by a positive point charge and that created by a negative point charge, they would look something like this. Notice that the difference is that the field lines point in toward the negative point charge but away from the positive charge. That tells us that, in our diagram, the blue dot is a negative charge since the field lines point in toward it.
But, of course, our question is not asking about the direction of the electric field, but rather the strength of it, its magnitude. And to figure that out, we can recall a relationship between the density of electric field lines and electric field strength. Electric field line density is directly proportional to electric field strength. That means if we’re in a region where there are lots of electric field lines, the electric field strength is greater in that region than somewhere else where there are fewer field lines.
That bears on our question because, notice, as we start out far away from our charge, the electric field line density is very low. There aren’t many field lines around this point. And by the way, we can just imagine extending the field lines we have out to infinity. So, we can’t draw them out to infinity, but we can draw them as far as the screen allows. Even drawing them that far, still the electric field line density around this particular point is fairly low.
But we see that as we move this point in, closer and closer to the charge, the field line density goes up. In other words, the spacing between electric field lines decreases as we get closer and closer in. According to our proposition, this means that the electric field strength is also getting higher and higher as we get closer into the charge. And that tells us that whichever of our three points — 𝑃, 𝑅, and 𝑆 — is closest to the central charge, that will be the point where the electric field is strongest.
Looking at these three points, it seems that point 𝑆 is farthest away. But maybe it’s about the same distance as point 𝑃. But definitely closer than either one of them is point 𝑅. Point 𝑅 is closest into the charge and, therefore, in the region of greatest electric field-line density and, therefore, in the region of greatest electric field strength. Point 𝑅 then is our answer. And we got to it by considering how far apart or close together the electric field lines are and how that correlates with electric field strength.