# Potential Difference and Electric Potential

• johnnyies
In summary, potential difference is the difference in electric potential between two points in an electric field, while electric potential is the electric potential energy per unit charge at a given point. Potential difference is directly proportional to electric potential, and both are measured in volts. The formula for calculating potential difference from an electric field is V = Ed. These concepts are significant in understanding electricity and play a crucial role in determining current flow and work in an electric circuit.
johnnyies

## Homework Statement

A uniform electric field of magnitude 375 N/C pointing in the positive x-direction acts on an electron, which is initially at rest. After the electron has moved 3.2 cm, what is

a. the work done by the field on the electron
b. change in potential energy associated with the electron
c. velocity of the electron

W = -qEd
KE = 1/2 mv^2

## The Attempt at a Solution

As far as math goes, I got all the answers, but I do not have the signs correct.

a. 1.92 x 10^-18 joules
b. -1.92 x 10^-18 joules
c. -2.05 x 10^6 m/s

I got those numbers, but the signs are entirely wrong. My book doesn't explain things very clearly. But what I'm confused about, is when an E field is pointing to the right, doesn't that mean the electron should move to the right? What does negative work mean? How does the electron lose potential energy?

Thanks.

Last edited:
johnnyies said:

## Homework Equations

W = -qEd
KE = 1/2 mv^2

Actually, W = +qEd. (The force is qE, and W=Fd.)

Okay, understood the equation mistake, but can someone answer my questions at the bottom?

johnnyies said:
But what I'm confused about, is when an E field is pointing to the right, doesn't that mean the electron should move to the right?

No. By definition, the direction of the electric field at a point is the direction in which a positive test charge would move if it were placed at that point. A negative charge would therefore move in the opposite of the field direction.

johnnyies said:
What does negative work mean?

If force and the displacement are in the opposite direction, then it is clear from the definition of work that the work done will be negative. The force acts to impede the existing motion, decelerating the particle. By the work-energy theorem, the work done is equal to the change in kinetic energy. Therefore, if negative work is done, the kinetic energy decreases. That's not what is happening in this situation though. In this situation, positive work is done and the charge is accelerated.

johnnyies said:
How does the electron lose potential energy?

Just as a mass raised to a certain height in a gravitational field has a certain potential energy, a charge located at a certain position within an electric field results in a system having a certain amount of electric potential energy. Conceptually, this potential energy can be thought of as the work that would have had to be done against the field in order to get the charge to that location. Just as when the mass is dropped and accelerates under gravity it loses potential energy (converted to kinetic) so too does charge lose potential energy (converted to kinetic) when accelerated by a field in the direction that it "wants" to go.

## 1. What is the difference between potential difference and electric potential?

Potential difference, also known as voltage, is the difference in electric potential between two points in an electric field. It measures the change in energy that a unit of charge experiences when moving from one point to another. Electric potential, on the other hand, is the electric potential energy per unit charge at a given point in an electric field. It is a scalar quantity and is measured in volts.

## 2. How is potential difference related to electric potential?

Potential difference is directly proportional to electric potential. This means that as the electric potential increases, so does the potential difference. Mathematically, potential difference (V) is equal to the electric potential (Φ) multiplied by the distance (d) between the two points: V = Φ x d.

## 3. What is the unit of measurement for potential difference and electric potential?

The unit of measurement for potential difference is volt (V), named after the Italian physicist Alessandro Volta. The unit of measurement for electric potential is also volt (V).

## 4. How do you calculate potential difference from an electric field?

Potential difference can be calculated from an electric field by using the formula V = Ed, where V is the potential difference, E is the electric field strength and d is the distance between the two points. This formula is derived from the relationship between potential difference and electric potential.

## 5. What is the significance of potential difference and electric potential in electricity?

Potential difference and electric potential are important concepts in understanding electricity. They help us understand how charges move in an electric field and how energy is transferred in an electric circuit. They are also crucial in determining the direction of current flow and the amount of work needed to move a charge between two points in an electric field.

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