OpenStax College Physics for AP® Courses, Chapter 18, Problem 50 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. This is the electric field in a charge distribution where you have negative 3q here and you have a single positive charge q over here. So this charge is of magnitude three times greater than this one and this one's negative and this one's positive. So couple of features to notice: one is that because this charge is three times greater, there are about 3 times more field lines going into this charge to represent the fact that the field should be three times greater and so if you count the field lines around the positive charge, it's one, two, three, four, five, six, seven field lines and around the negative 3q charge, it's one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen so approximately three times as many field lines because that density of field lines represents the field strength. The arrows are pointing towards the negative charge because a positive test charge placed here would be attracted towards this negative charge and the field line point in the direction of force that a positive test charge would experience. And when field lines are emanating away from this positive charge... you know, when you are close to the positive charge that closeness means that the positive charge will have a strong electric field because the field depends a lot on distance since electric field is kq over r squared— having a small distance makes a big difference. And so really close to the positive q charge, you basically see radial field lines emanating out but when you are some distance away, now the fact that this charge over here is of 3 times greater magnitude that begins to matter and so the field lines quickly turn towards this negative 3q charge. And so if the charges were of equal magnitude, you would expect field lines that were like... kind of like semi-circles... it would make an oval like this if they were of equal magnitude but because this negative charge is of greater magnitude then you have this shape where it goes up and then has a bit of a shoulder here and then goes down like this and for quite some distance from the negative 3q charge, we expect to see field lines that are coming in radially and so this is the effect that you see. Okay and there we go!