# Change in potential energy of the particle

• zohaibtarar
In summary: Your final numerical result is correct, but the units should be J, not eV. In summary, the change in potential energy of a particle with a charge of 2e moving between two points with a potential difference of 75V is 2.403×10⁻¹⁷ J. This can be calculated using the formula ΔU = q ΔV, where ΔV is the potential difference and q is the charge of the particle.
zohaibtarar

## Homework Statement

A particle with a charge of 2e moves between two points which have a potential difference of 75V. What is the change in potential energy of the particle?

U = (75 V)(2e)

## The Attempt at a Solution

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When a particle with charge e moves through a potential difference of 1 volt, the change in potential energy is 1 eV. If the charge is some multiple of e—say Ne—the change in potential energy in electron volts is N times the potential difference in volts. Note: 1 eV = 1.602 x 10⁻¹⁹ J.

Potential is potential energy per unit charge. We define the potential V at any point in an electric field as the potential energy U per unit charge associated with a test charge q₀ at that point:

V = U/q₀
U = Vq₀
U = (75 V)(2e)
U = 150 eV
U = 150(1.602 x 10⁻¹⁹ J)
U = 2.403×10⁻¹⁷ J Solution: U = 150 eV = 2.403×10⁻¹⁷ Jjust need to make sure if i did this correctly? or do i need todo anything else?

Thank you

OK. But be sure you understand that you are not finding the potential energy U itself. You are calculating the change in potential energy ΔU. The appropriate relation would be written ΔU = q ΔV, where ΔV is the potential difference.

## 1. What is potential energy and how does it change in a particle?

Potential energy is the energy that an object possesses due to its position or configuration. The change in potential energy of a particle can occur when its position changes, such as when it moves from a higher elevation to a lower elevation in a gravitational field. This change is equal to the difference in potential energy between the two positions.

## 2. What factors can cause a change in potential energy of a particle?

There are several factors that can cause a change in potential energy of a particle, including its position, its mass, and the type of force acting on it. For example, a particle's potential energy will increase as it moves to a higher position in a gravitational field, and it will decrease as it moves to a lower position. Additionally, the mass of a particle can affect its potential energy, as heavier particles will have a greater potential energy than lighter particles in the same position. Finally, different types of forces, such as gravitational or electric, can also cause changes in potential energy of a particle.

## 3. How can the change in potential energy of a particle be calculated?

The change in potential energy of a particle can be calculated using the equation ΔU = U2 - U1, where ΔU represents the change in potential energy, U2 represents the potential energy at the final position, and U1 represents the potential energy at the initial position. This equation can be used for both gravitational and electric potential energy.

## 4. Can the change in potential energy of a particle be negative?

Yes, the change in potential energy of a particle can be negative. This occurs when the particle's potential energy decreases, such as when it moves from a higher position to a lower position. Negative changes in potential energy can also occur when a force does negative work on the particle, meaning it decreases the particle's energy rather than increasing it.

## 5. How does the change in potential energy of a particle relate to its kinetic energy?

The change in potential energy of a particle and its kinetic energy are related through the law of conservation of energy. This law states that energy cannot be created or destroyed, only transferred or converted from one form to another. When a particle's potential energy decreases, its kinetic energy will increase by the same amount, and vice versa. This means that the total energy of the particle (potential energy + kinetic energy) remains constant.

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