OpenStax College Physics for AP® Courses, Chapter 19, Problem 40 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. The charge q 1 has a charge of negative 3q whereas this charge on the right hand side has a charge of positive q. Now the field lines are emanating away from the positive charge and towards the negative charge— and that is the blue electric field lines I am talking about here— and we are meant to draw some equipotential lines. So one thing to keep in mind is that equipotential lines are perpendicular to the electric field lines and the reason for that is that it would take no work to move a charge from one position on this equipotential line to another position on that equipotential line because this charge would be going perpendicular to the electric field and so the electric field would have no component of force in the direction of motion along this equipotential line. And so since the field isn't doing any work that means there is no change in potential energy associated with the electrostatic force. Another thing to notice is that potential is increasing going from the negative to the positive charge and the spacing between the equipotential lines is really close together where there's a high density of electric field lines because where the electric field lines are close together that means the field is stronger and so there's more work done traveling along the field where the field is strong. And so the equipotential lines should be closer together because the spacing... well, each equipotential line is meant to be a certain interval of potential compared to the other so this might be a difference of 10 volts or something— I am just making up the number 10 but some number that is consistent— so this would be another 10 volt difference and this would be another 10 volt difference but when the field is weak like way out here, you need to go really far in order to have that field do 10... you know... well, 10 volts per coulomb or 10 joules per coulomb of work; a volt being joules per coulomb. Okay. So it's intentional to have a large spacing over here and a small spacing over here and the spacing close to the negative 3q charge is smaller than the spacing close to the q 2 charge and yeah, I think that's about all we need to say.