# Potential Difference between 2 points

1. Dec 6, 2015

### qlzlahs

1. The problem statement, all variables and given/known data
A +4.0 μC-point charge and a -4.0 μC point charge are placed as shown in the figure. What is the potential difference, V_A - V_B, between points A and B? (k = 1/4πε_0 = 8.99 × 10^9 N · m^2/C^2)

https://www.physicsforums.com/attac...2/?temp_hash=fc256c7e6e7317423fc360366b1c7272

2. Relevant equations
V = (k*q)/r

3. The attempt at a solution
Point B is 0.30 m away from the -4.0 μC point charge. The potential there is (9*10^9*-4*10^(-6))/(.3) = -120,000 V.
Point A is 0.30 m away from the 4.0 μC point charge. The potential there is (9*10^9*4*10^(-6))/(.3) = 120,000 V.
So I thought I could do V_A - V_B = 120,000V - (-120,000V) = 240,000V but that doesn't work.

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2. Dec 6, 2015

### QuantumQuest

The point here is to create the algebraic sum of potential differences between points A and B. So, what about between the two charges?

3. Dec 6, 2015

### Staff: Mentor

You need to account for the potentials due to both charges at both locations. So for example the potential at point A is due to the effects of both the 4 μC charge and the -4 μC charge combined.

4. Dec 6, 2015

### qlzlahs

So the potential at A is:
(9*10^9*4*10^(-6))/(.3) + (9*10^9*-4*10^(-6))/(.5) = 48,000 V
and the potential at B is:
(9*10^9*-4*10^(-6))/(.3) + (9*10^9*4*10^(-6))/(.5) = -48,000 V
V_a - V_b = 96,000 V?

5. Dec 6, 2015

### Staff: Mentor

That looks better.

6. Dec 6, 2015

### qlzlahs

Thanks! Got it.