2
$\begingroup$

Problem: Imagine a sphere of radius a filled with a negative charge density equal of two electron charge. Embedded in this is two protons, assume that the negative charge distribution remains uniform in spite of the presence of the two protons. Where must the protons be located so that the net force on them is zero?

This one has stumped me, my friend and a colleague. By Guass's Law, the field inside is 0? So, if I place one proton inside, it will not experience any force $$qE = 0$$ but if there are two protons inside, they will interact with each other. So they must be placed in some kind of symmetrical fashion so that the forces cancel?

$\endgroup$
3
  • 1
    $\begingroup$ Why do you say that by Gauss's Law th field inside is zero? $\endgroup$
    – DoeJohn
    Nov 1, 2019 at 18:54
  • $\begingroup$ I assumed all of the charge was on the outside surface. $\endgroup$
    – mushin
    Nov 1, 2019 at 19:19
  • 1
    $\begingroup$ Then there is no place inside the sphere where they can be at rest, because each proton would feel the repulsion of the other one and no other force to counteract it, so it would move accordingly $\endgroup$
    – DoeJohn
    Nov 1, 2019 at 19:29

1 Answer 1

1
$\begingroup$

A charge distribution spread over the volume of a sphere does not have zero field everywhere. Most texts invite students to prove that the field inside a uniform sphere of charge is linear in the distance from the center.

Your phrasing suggests you are imagining a spherical shell of charge, which has zero electric field on the inside.

$\endgroup$
1
  • $\begingroup$ Thank you. This gives an idea for a solution. $\endgroup$
    – mushin
    Nov 1, 2019 at 19:20

Not the answer you're looking for? Browse other questions tagged or ask your own question.