# Electric Potential Energy

on . Posted in Electrical Engineering

Electric potential energy, abbreviated as $$U_e$$, also called electrostatic potential energy, is the energy stored in a system of charged particles due to their relative positions in an electric field.  It arises from the interactions between charges and is a fundamental concept in electromagnetism.  Electric potential energy is associated with the potential difference, or voltage, between points in an electric field.

The electric potential energy of a system of charges is influenced by the arrangement and distribution of charges in the electric field.  Charges with the same sign tend to repel each other and have higher potential energy when brought closer.  Charges with opposite signs attract each other and have lower potential energy when brought closer.

When a charge is moved within an electric field, its electric potential energy can change.  If work is done to move a charge against the electric field, its potential energy increases.  Conversely, if a charge moves in the direction of the electric field, its potential energy decreases.  Electric potential energy is closely related to electric potential, which is a scalar field that describes the potential energy per unit charge at a point in space.  The electric potential difference (voltage) between two points is the change in electric potential energy per unit charge as a charge is moved between those points.

### Electric Potential Energy formula

$$U_e = k_e \; q_1 \; q_2 \;/\; r$$

$$k_e = U_e \; r \;/\; q_1 \; q_2$$

$$q_1 = U_e \; r \;/\; k_e \; q_2$$

$$q_2 = U_e \; r \;/\; k_e \; q_1$$

$$r = k_e \; q_1 \; q_2 \;/\; U_e$$

Symbol English Metric
$$U_e$$ = electric potential energy $$lbf-ft$$ $$J$$
$$k_e$$ = Coulomb's constant (see physics constants) $$constant$$
$$q_1$$ = magnitude of the point electric charge $$C$$ $$A-s$$
$$q_2$$ = magnitude of the point electric charge $$C$$ $$A-s$$
$$r$$ = seperation distance between the charges $$ft$$ $$m$$

Tags: Energy