Question

Consider eight +Q point charges distributed equidistantly on a circle of radius R. What is the electric potential energy of a point charge +Q placed at the center of the circle due to the eight other +Q point charges?

Answer 1

The electric potential energy felt by charge q as a result of another charge of charge Q is
\[U=\frac{ qQ }{ 4\pi \epsilon _{0}r }\]
Where r is the distance between the two charges q and Q.

The electrostatic potential energy stored in the system of eight charges as in your question, with respect to a central charge would be:

\[U=\frac{ 1 }{ 4\pi \epsilon _{0} }\sum_{n=1}^{8}(\frac{ Q _{n}Q _{c} }{ r })\]

where Q_n is the charge of the outer particles and Q_c is the charge of the central particle.

Given that all the charges have the same charge, +Q, this can be expressed as
\[U=\frac{ 8Q^{2} }{ 4\pi \epsilon _{0}r }\]
or
\[U=\frac{ 4Q^{2} }{ \pi \epsilon _{0}r }\]

Answer 2

8/4 is not 4

Answer 3

it's 2 :))

Answer 4

laughing out loud you're so smart

Answer 5

i know >:p

Answer 6

Yeah you're right, it's always the simple arithmetic that gets me :1