# Work done by an electric field

• skwz
In summary, the conversation discusses a scenario where two charged rods, each with a net charge -Q, are held in place, and a small test charge -q travels from point X to point Y along a circular arc. The direction of the electric force on the test charge at points X and Y is shown by arrows in the diagram. The question is asked whether the work done on the charge by the electric field is positive, negative, or zero. After analyzing the forces and angles involved, it is concluded that the work done by the electric field from the right hand rod is positive, while the work done by the electric field from the left hand rod is zero. However, there is some confusion regarding the direction of the electrostatic force and
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

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

#### Attachments

• physics2.jpg
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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?

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!

## 1. What is meant by work done by an electric field?

The work done by an electric field is the amount of energy transferred to a charged particle as it moves through the electric field. It is a measure of the force exerted by the electric field on the charged particle over a certain distance.

## 2. How is work done by an electric field calculated?

The work done by an electric field can be calculated using the formula: W = qV, where q is the charge of the particle and V is the potential difference between two points in the electric field.

## 3. What is the unit of measurement for work done by an electric field?

The unit of measurement for work done by an electric field is joules (J). This is the same unit used to measure other forms of energy.

## 4. Can the work done by an electric field be negative?

Yes, the work done by an electric field can be negative. This occurs when the direction of the electric field is opposite to the direction of the charged particle's motion, resulting in the particle losing energy.

## 5. How does the work done by an electric field affect the velocity of a charged particle?

The work done by an electric field can either increase or decrease the velocity of a charged particle, depending on the direction of the electric field and the direction of the particle's motion. If the electric field and particle's motion are in the same direction, the work done will increase the particle's velocity. If they are in opposite directions, the work done will decrease the particle's velocity.

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