# Electrostatics - point charges and work

1. Mar 8, 2012

### HenryHH

Electrostatics -- point charges and work

1. The problem statement, all variables and given/known data

A 3.0 μC point charge and a 9.0 μC point charge are initially infinitely far apart. How much work
does it take to bring the 3.0 μC point charge to x = 3.0 mm, y = 0.0 mm and the 9.0 μC point charge to x = -3.0 mm, y = 0.0 mm? (The value of k is 9.0 × 109 N∙m2/C2.)

q1 = 3.0 uC, q2 = 9.0 uC, k = 9.0 × 109 N∙m2/C2

2. Relevant equations

F = k(q1)(q2)/r^2

3. The attempt at a solution

I know the answer is 41 J (this is just a practice problem). I'm assuming that the formula F = k(q1)(q2)/r^2 is supposed to be used because I have values for most variables, but I'm not sure what the radius would be. If one point charge is at x = 3mm and the other point charge is at x = -3mm, then is the radius 6 mm (I got this value by counting along the x-axis)? Also, how would the answer end up being in Joules?

2. Mar 8, 2012

### issacnewton

Re: Electrostatics -- point charges and work

When two discrete charges are brought together, the amount of work one has to do is just the energy which gets stored in the system. Energy stored for two charges is

$$U=\frac{k_e q_1 q_2}{r}$$

where r is the distance between the two charges. Using the coordinates of the two charges given, you can find the distance between them. Since work done is same as the energy
transfer, it has the same unit as the energy