# Homework Help: Electric Potential Difference

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1. Feb 14, 2017

### jlmccart03

1. The problem statement, all variables and given/known data
Two charged rods, each with net charge -Q0 are held in place as shown in the top view diagram below.

a. A small test charge -q0 travels from point X to point Y along the circular arc shown.
i. Draw an arrow on the diagram at each point to show the direction of the electric force on the test charge at that point. Explain why you drew the arrows as you did.

ii. Is the work done on the charge by the electric field positive, negative, or zero? Explain.

iii.Is the electric potential difference ΔVx→y positive, negative, or zero? Explain.

b. The test charge is launched from point X with an initial speed v0 and is observed to pass through point Y. Is the speed of the test charge at point Y grater than, less than, or equal to v0? Explain.

2. Relevant equations
W = -ΔVq
ΔV = Vf-Vi
3. The attempt at a solution
For the first part (i) as shown in the diagram I drew the arrows based on the two forces and did vector addition to get the resulting vector.

For the second part (ii) I say it is negative work since you are moving the charge in a direction it wants to go so it is negative work done.

For the third part (iii) I really don't know what I am supposed to look at here besides that the electric potential must be positive (possibly) I really don't understand how to look at a diagram and figure this piece out.

The final part (b) I say the speed is greater than the speed v0 since the charge is going where it wants to so it has a force to go that direction increasing its acceleration.

2. Feb 14, 2017

### cnh1995

What does this tell you about the force acting on the test charge?

3. Feb 14, 2017

### jlmccart03

The force is different at all points along the arc since they are all at different distances from the two other -Q charges correct?

4. Feb 14, 2017

### haruspex

Ok, but you could get the directions a little more accurate by taking into account the proximities of the charges when drawing the force vector lengths.
That may be true towards the end of the path, but it is certainly not true at the start. Can you think of a way to answer it just by considering the start and end points, not worrying about the path?
This is really the same as part ii). Which of X and Y is at the higher potential?
Nothing. There is no suggestion that the motion is purely in response to the electric field. Indeed, it could not be.