How Does Charge Movement Affect Electric Potential and Kinetic Energy?

[jlmccart03]

Homework Statement

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 ΔV_x→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.

Homework Equations

W = -ΔVq
ΔV = V_f-V_i
Vector addition

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.

 

[cnh1995]

A small test charge -q0 travels from point X to point Y along the circular arc shown.

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

 

[jlmccart03]

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

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

 

[haruspex]

drew the arrows based on the two forces and did vector addition

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.

negative work since you are moving the charge in a direction it wants to go

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?

For the third part (iii) I really don't know what I am supposed to look at here

This is really the same as part ii). Which of X and Y is at the higher potential?

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

Nothing. There is no suggestion that the motion is purely in response to the electric field. Indeed, it could not be.