Work done by an electric field

[skwz]

Homework Statement

Two charged rods, each with a net charge -Q are held in place as shown in the top view diagram.

a) A small test charge -q travels from point X to pt. Y along a circular arc shown.

i) Draw an arrow on the diagram at each pt. (X & Y) to show the direction of the electric force on the test charge at that point​

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

Diagram --> http://img136.imageshack.us/img136/2262/physics2ai4.png

Homework Equations

F = q(source)E
W = Fd cos (theta)
W = q(source) Ed cos(theta)

The Attempt at a Solution

Was wondering if my answers made sense. Thanks again

a.) My reasoning for the direction is that each rod exerts an electrostatic force on the charge at points X and Y that are directed away from the charge. After drawing respective components for each force, I arrived at my present answer (in the diagram link)

b.) Here is where I'm at odds. I figured that the work due to the electric field from the left rod is zero since the electric field vector and displacement vector are perpendicular at every point along the path. Therefore the net work is only due to the right hand rod. I think the work done is positive since the electric field vectors from the right hand rod and the displacement vectors form an angle greater than 90 since the electric field is directed inwards toward the rod. However since the electrostatic force is repulsive between the right hand rod and test charge, then the electrostatic force is in the opposite direction of electric field. Thus the electrostatic force vector and displacement vector form an angle less than 90 and therefore positive work is done by the electric field from second equation. Is my reasoning logical or is there something I'm missing. Thanks

 

[skwz]

Hmmm.. my textbook says that if a negatively charge particle accelerates in a direction opposite to the electric field, the charge field system looses electric potential and electric potential energy is positive. If that's true, then by the conservation of energy, kinetic energy decreases and thus work is negative? I'm really confused now... anyone?

 

[Moetasim]

I would like to commend you on your thorough understanding and reasoning for this problem. Your answers are correct and make perfect sense.

In part b), you are correct in saying that the work done by the electric field from the left rod is zero since the displacement vector and electric field vector are perpendicular. This means that the component of the electric force in the direction of displacement is also zero, resulting in no work done.

For the right rod, the work done by the electric field is positive because the displacement vector and electric field vector are not perpendicular, and thus there is a component of the electric force in the direction of displacement. Your reasoning for the angle formed by the electrostatic force and displacement vector is also correct.

Overall, your understanding and explanation of the concept of work done by an electric field is very clear and accurate. Well done!