Electric Potential Energy Calculator
Enter two charges, the distance between them and permittivity to compute their electric potential energy U = k·q1·q2/r.
Input Data
Results
At a glance:Electric (electrostatic) potential energy U is the work needed to assemble a configuration of charges. For two point charges U = (1/(4πε))·q1·q2/r = k·q1·q2/r with k = 1/(4πε₀) ≈ 8.988×10⁹ N·m²/C². In vacuum ε = ε₀; in a dielectric ε = ε₀·ε_r. Like charges give U>0 (you must do work to bring them together); opposite charges give U<0 (they attract). For many charges sum all pairwise terms. This energy is released or absorbed in chemical bonds and atomic transitions.
Formula
U = k·q1·q2/r
k = 1/(4πε) ≈ 8.988×10⁹ N·m²/C²
$$U = \frac{k \, q_1 q_2}{r}$$How to Use
- Enter charges q1 and q2 (C).
- Enter the separation r (m) and permittivity ε.
- The calculator returns U.
Case Studies
Two protons 1 nm apart
q1 = q2 = 1.6×10⁻¹⁹ C, r = 1×10⁻⁹ m.
U ≈ 8.988e9×(1.6e-19)²/1e-9 ≈ 2.3×10⁻¹⁹ J (≈1.44 eV).
Repulsive; energy is released if they move apart.
FAQ
Why is potential energy negative for opposite charges?
Bringing opposite charges together lowers the system energy (they attract), so the stored potential energy is negative relative to infinite separation.
What role does permittivity play?
A higher permittivity (e.g. in a dielectric) weakens the interaction, reducing U for the same charges and distance.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.