What is the electric potential energy between two protons each of charge q and at a distance of r apart? (Permittivity of free space = εo)
4πεoq2r
qr/4πεo
q/4πεor
q2/4πεor
q2/4πεo
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Electric potential at any point in an electric field is the work done in bringing a unit positive charge from infinity to that point against electrical forces of the field
V=Work done/Charge
but work done=force * distance FD
therefore V=FD/q
but force in an electric field= q1q2/4π£r²
and distance= r
therefore V = q1q2/4π£r² * r / q
q1=q2=q
therefore V=q²*r / 4π£r² * q
r² divide r = r
q² divide q = q
V= q / 4π£r

I believe the answer should be D, based on the question description of the formula.

if you are still confused on the answer. the formular for finding the force charge between two bodies is iven by
q1*q2/4πεor. In the question, it was said that q1 and q2 have equal charges which means q1=q2 so q=q2
then q2/4πεor D. hope this helps

