Electric Potential Energy (U)

Definition and Analogy

Electric potential energy is the energy associated with a charged particle due to its location in an electric field. This concept is analogous to gravitational potential energy, which is the energy associated with a mass due to its location in a gravitational field:

• Gravitational potential energy:

• Electric potential energy (uniform field):

Here, is the charge, is the magnitude of the electric field, and is the position relative to a reference point (often ).

Key Properties of Electric Fields and Charges

• Opposites attract; like charges repel.

• Electric field direction: Points away from positive charges and towards negative charges. (A useful mnemonic: "What would a proton do?")

• Motion in electric fields: A particle in an electric field always moves towards a lower potential energy.

Electric Potential Energy - Examples

Proton in a Uniform Electric Field

Consider a proton located in a uniform electric field of magnitude created by a negatively charged plate, at a distance from the plate.

• Formula:

• Calculation:

• Direction of motion: The proton will move downwards (towards the plate).

• Change in potential energy: The potential energy decreases as the proton gets closer to the plate; this energy is converted into kinetic energy.

Electron in a Uniform Electric Field

Consider an electron in the same field and position as above.

• Formula:

• Calculation:

• Direction of motion: The electron will move upwards (away from the plate).

• Change in potential energy: The potential energy decreases (becomes more negative) as the electron moves farther from the plate; this energy is also converted into kinetic energy.

Summary Table: Electric Potential Energy for Proton vs. Electron

Conceptual Notes

• For both protons and electrons, movement in the electric field is towards lower potential energy.

• The sign of the charge determines the direction of force and motion in the field.

• Potential energy lost by the particle is gained as kinetic energy.

Additional info:

• In a uniform electric field, the potential energy change is linear with displacement .

• Reference position () is typically chosen at the plate for convenience in calculations.