Calculator Form
Choose a mode, enter your values, and calculate electric potential energy using charge interactions, potential, energy change, or capacitor storage formulas.
Formula Used
1) Two Point Charges
Formula: U = kq₁q₂ / r
Use this when two point charges are separated by a known distance. Here, k = 8.9875517923 × 10⁹ N·m²/C².
2) Charge at a Potential
Formula: U = qV
Use this when a charge is placed at a known electric potential. Positive and negative signs matter.
3) Change in Potential Energy
Formula: ΔU = q(Vf - Vi)
This calculates the energy gained or lost when a charge moves between two potentials.
4) Capacitor Energy
Formulas: U = ½CV², U = Q²/(2C), U = ½QV
These equivalent forms calculate the energy stored in an ideal capacitor, depending on which values are known.
How to Use This Calculator
Step 1
Select the calculation mode that matches your problem: point charges, potential, energy change, or capacitor storage.
Step 2
Enter the known values and choose the correct units for charge, distance, voltage, and capacitance.
Step 3
Press the calculate button. The result appears above the form and below the header with interpretation and conversions.
Step 4
Use the CSV and PDF export buttons to save your result. Review the graph to understand the energy trend.
Example Data Table
| Scenario | Inputs | Formula | Result |
|---|---|---|---|
| Two point charges | q₁ = 3 µC, q₂ = -5 µC, r = 0.20 m | U = kq₁q₂ / r | -0.674066 J |
| Charge at a potential | q = 2 µC, V = 1500 V | U = qV | 0.003 J |
| Change in energy | q = -4 µC, Vi = 120 V, Vf = -80 V | ΔU = q(Vf - Vi) | 0.0008 J |
| Capacitor energy | C = 47 µF, V = 12 V | U = ½CV² | 0.003384 J |
FAQs
1) What is electric potential energy?
Electric potential energy is the stored energy associated with the position of charges in an electric field. It tells you how much work is required to move charges between locations or assemble a charge configuration.
2) How do I calculate electric potential energy between two point charges?
Use U = kq₁q₂ / r. Multiply Coulomb’s constant by both charges, then divide by the separation distance. The sign shows whether the interaction is attractive or repulsive.
3) How to calculate change in electric potential energy?
Use ΔU = q(Vf - Vi). Subtract the initial potential from the final potential, then multiply by the charge. A positive result means energy increased, while a negative result means energy was released.
4) What does a negative electric potential energy result mean?
A negative result means the configuration is energetically favorable compared with the chosen reference. For opposite charges, it usually means attraction and that energy must be added to separate them farther apart.
5) How does distance affect electric potential energy?
For two point charges, electric potential energy varies inversely with distance. Doubling the separation cuts the magnitude in half. Halving the separation doubles the magnitude, assuming the charges stay the same.
6) Which capacitor energy formula should I use?
Use U = ½CV² when capacitance and voltage are known. Use U = Q²/(2C) when charge and capacitance are known. Use U = ½QV when charge and voltage are known.
7) Calculate the electric potential energy in a capacitor that stores 9.40.
If the capacitor stores 9.40 joules, its electric potential energy is 9.40 J. If 9.40 refers to capacitance or voltage, combine it with another known value using a capacitor energy formula.
8) Which units should I enter in this calculator?
You can enter charges in C, mC, µC, or nC; distances in m, cm, or mm; voltages in V, kV, or mV; and capacitance in F, mF, µF, nF, or pF.