# How Does Charge Movement Affect Electric Potential and Kinetic Energy?

• jlmccart03
In summary: The test charge is travelling in a circle, and a constant electric field can only produce an acceleration in a straight line.In summary, the conversation discusses the movement of a small test charge -q0 between two charged rods with a net charge of -Q0. The direction of the electric force on the test charge is determined by vector addition, and the work done on the charge by the electric field is negative as the charge is moving in a direction it wants to go. The electric potential difference ΔVx→y is also negative, indicating a decrease in potential as the charge moves from X to Y. The final part discusses the speed of the test charge, which is greater than its initial speed v0 due to the force acting on
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 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.

W = -ΔVq
ΔV = Vf-Vi

## 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.

jlmccart03 said:
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?

cnh1995 said:
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?

jlmccart03 said:
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.
jlmccart03 said:
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?
jlmccart03 said:
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?
cnh1995 said:
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.

## 1. What is electric potential difference?

Electric potential difference, also known as voltage, is the difference in electric potential energy between two points in an electric field. It is measured in volts (V) and represents the amount of work needed to move a unit of charge from one point to another.

## 2. How is electric potential difference different from electric potential?

Electric potential difference is a measure of the difference in potential energy between two points, while electric potential is a measure of the potential energy at a specific point in an electric field. In other words, electric potential difference takes into account both the starting and ending points, while electric potential only considers the ending point.

## 3. What causes electric potential difference?

Electric potential difference is caused by the presence of an electric field. This field is created by the separation of positive and negative charges, and the potential difference is a result of the force exerted by this field on charged particles.

## 4. How is electric potential difference measured?

Electric potential difference can be measured using a voltmeter, which is a device that measures the difference in electric potential between two points in an electric circuit. The voltmeter is connected in parallel to the points being measured, allowing for an accurate measurement of the potential difference.

## 5. What are some practical applications of electric potential difference?

Electric potential difference has many practical applications, including powering electronic devices, providing electricity to homes and buildings, and charging batteries. It is also used in various technologies such as motors, generators, and power grids.

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