0.359502
J
2.2438e+18
eV
7.19
N
1
2.00000000e-12
C^2
0.359502
J
2.2438e+18
eV
7.19
N
1
2.00000000e-12
C^2
The Electric Potential Energy Calculator computes the electrostatic potential energy stored in a system of two point charges. Electric potential energy represents the work required to assemble a charge configuration by bringing charges from infinity to their final positions. For two point charges, the potential energy is given by $$U = k\frac{q_1 q_2}{r}$$, where k is Coulomb's constant and r is the separation distance. Unlike kinetic energy, potential energy can be positive or negative: positive when like charges are brought together (energy must be supplied against the repulsive force), and negative when opposite charges are brought together (energy is released as the attractive force does work). This concept is essential in understanding atomic structure, chemical bonding, nuclear physics, and energy storage in electric fields. The calculator also converts the energy to electron volts and computes the corresponding electrostatic force.
The electric potential energy of a two-charge system is:
$$U = k\frac{q_1 q_2}{r} = \frac{q_1 q_2}{4\pi\varepsilon_0 r}$$
where:
Key properties:
The force is the negative gradient of the potential energy: $$F = -\frac{dU}{dr} = k\frac{q_1 q_2}{r^2}$$. The energy is also expressed in electron volts (eV) where 1 eV = 1.602 × 10⁻¹⁹ J, a unit natural for atomic-scale energies. For a system of N charges, the total energy is the sum over all unique pairs: $$U_{total} = \sum_{i
Positive potential energy indicates that the system is in a repulsive configuration — releasing the charges would convert this stored energy into kinetic energy as they fly apart. Negative potential energy means the charges are in an attractive, bound configuration — you would need to supply energy to separate them to infinity. The magnitude of the energy indicates the strength of the electrostatic interaction. The electron volt conversion is particularly useful for comparing with atomic and molecular energy scales: chemical bond energies are typically 1–10 eV, while nuclear binding energies are in the MeV range. The force output shows the instantaneous force between the charges at the given separation.
Inputs
Results
Two positive charges (1 μC and 2 μC) at 5 cm apart store 0.36 J of electrostatic potential energy. This positive energy means work was required to bring them together, and they would repel if released. The force between them is 7.19 N.
Inputs
Results
A +4 μC and −3 μC charge at 2 cm apart have a potential energy of −5.39 J. The negative sign indicates a bound system — these charges attracted each other as they were brought together, releasing 5.39 J. Separating them back to infinity would require 5.39 J of external energy.
Negative electric potential energy means the charge configuration is in a bound state — the charges attracted each other during assembly, and energy was released. To separate the charges back to infinity, you must supply energy equal to |U|. This is analogous to gravitational potential energy being negative for bound orbits. An atom's electron has negative potential energy due to its attraction to the positive nucleus.
Electric potential (V) is energy per unit charge at a point in space, measured in volts (J/C). Potential energy (U) is the total energy of a specific charge configuration, measured in joules. For two charges: U = q₁V₂ = q₂V₁, where V₂ is the potential created by q₁ at the location of q₂. Potential is a field property; potential energy is a system property.
The energy is stored in the electric field itself. The energy density at any point in an electric field is u = ½ε₀E², and integrating this over all space gives the total potential energy. This field-energy perspective is fundamental in electromagnetic theory and is essential for understanding electromagnetic waves, which carry energy through their fields.
An electron volt is the energy gained by an electron accelerated through a potential difference of 1 volt: 1 eV = 1.602 × 10⁻¹⁹ J. It is a convenient unit for atomic and subatomic physics. Typical atomic ionization energies are 1–25 eV, chemical bond energies are 1–10 eV, and nuclear binding energies are in the MeV (10⁶ eV) range.
For N charges, calculate the potential energy for every unique pair and sum them: U = Σᵢ<ⱼ kqᵢqⱼ/rᵢⱼ. For three charges, there are three pairs. For four charges, six pairs. The total energy represents the work required to assemble the entire configuration from infinity, bringing charges in one at a time.
Force is the negative spatial derivative (gradient) of potential energy: F = −dU/dr. In electrostatics, this gives Coulomb's Law from the potential energy expression. The force always points in the direction of decreasing potential energy — charges naturally move to lower their potential energy. At equilibrium points, the force is zero and the potential energy has a local extremum.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
Coulomb's Law Calculator
Electrostatics Calculators
Electric Field Calculator
Electrostatics Calculators
Electric Potential Calculator
Electrostatics Calculators
Capacitance Calculator
Electrostatics Calculators
Capacitor Energy Calculator
Electrostatics Calculators
Capacitors in Series Calculator
Electrostatics Calculators
