Question

Two point charges 2.5 cm apart have an electric potential energy -150 uJ. The total charge is 27 nC. What are the two charges?

Answer 1

Call the two charges q1 and q2. We know the sum of them q1 + q2 = 27 x 10^-9 C

Fix one of the charges in space. Now take the other charge and bring it in to the other charge from infinity (where the energy state of the system is zero). The work required to be done is
\[ W = \int_{\infty}^{0.025 \ m} \frac{kq_1q_2}{r^2} dr \ \ . \] That work is equal to the energy of the system, E = -150 x 10^-3 Joules.

Evaluate that integral and find the a new expression for q1 and q2. Use it together with the first expression involving these two variables to solve for q1 and q2.

Answer 2

I think im doing it wrong because the q keeps cancels them out.

Answer 3

Just to let you know that \[1\mu J=10^{-6}J\]

Answer 4

Yes, sorry, I should have written 10^-6, not 10^-3.

In any case, that integral is equal to
\[ W = - \frac{kq_1q_2}{0.025} \] and that must be equal to the energy level of the system. Now you have the second equation in q1 and q2. Find an expression for one of them in terms of the other and substitute it into the first equation and solve.

Answer 5

You are doing excellent work James. You're a machine on this thing! :)

Answer 6

I'm hoping if I keep on kicking on the start motor, we will get enough critical mass of competent answers that it will become self-sustaining.

Answer 7

:)