Calculator
Choose one mode. Enter the matching fields. Unused fields are ignored.
Formula Used
Point charge potential: V = kQ / (εᵣr).
Pair potential energy: U = kq₁q₂ / (εᵣr).
Energy at potential: U = qV.
Potential from work: V = W / q.
Energy change: ΔU = q(Vᵦ − Vₐ).
Many charges: Vtotal = (k / εᵣ)Σ(Qᵢ / rᵢ).
Capacitor storage: U = ½CV².
How to Use This Calculator
- Select the calculation mode that matches your problem.
- Enter charge, distance, voltage, work, or capacitance values.
- Pick the correct units for each input group.
- Set relative permittivity for the medium.
- Press Calculate to show results above the form.
- Use CSV or PDF buttons for saved records.
Example Data Table
| Mode | Inputs | Expected idea |
|---|---|---|
| Pair energy | q₁ = 5 µC, q₂ = -2 µC, r = 15 cm | Negative energy shows attraction. |
| Point potential | Q = 8 µC, r = 10 cm | Potential is positive near positive charge. |
| Potential difference | q = 3 µC, Vₐ = 0 V, Vᵦ = 120 V | Energy change equals qΔV. |
| Capacitor energy | C = 220 µF, V = 12 V | Stored energy equals one half CV². |
Electric Potential Concepts
Electric potential describes energy per unit charge. It shows how strongly a source charge can push or pull another charge. The value depends on charge size, distance, and medium. A positive source creates positive potential nearby. A negative source creates negative potential nearby. The sign matters in every calculation.
Electric potential energy describes stored interaction energy. Two like charges have positive potential energy. They resist being pushed together. Opposite charges have negative potential energy. They release energy as they move closer. This calculator keeps signs visible, so interpretation stays clear.
Why Distance Matters
Point charge equations use inverse distance. Doubling distance halves potential. It also halves pair potential energy. Very small distances can create very large values. That is normal for ideal point charge models. Real objects have size, shape, and charge spread. Use realistic distances for better physical meaning. Distance should be measured between charge centers. Surface spacing can give wrong answers.
Medium And Relative Permittivity
A medium changes electric interaction strength. Vacuum and dry air have relative permittivity near one. Water and many dielectrics reduce the effective potential. The calculator divides Coulomb constant by relative permittivity. This gives a simple dielectric correction. Advanced laboratory work may need geometry specific models. Materials can be frequency dependent too. Temperature may also affect permittivity values.
Work, Voltage, And Energy
Potential difference links force ideas with energy ideas. If a charge moves through voltage, its energy changes. The relation is simple. Energy change equals charge times potential difference. Work done per unit charge gives electric potential. These ideas explain batteries, capacitors, electron beams, and sensors. Sign convention still remains important. Positive work can raise electric potential energy.
Multiple Source Charges
Electric potential is a scalar quantity. Potentials from many charges add directly. Direction is not needed for potential addition. Each source contributes kQ divided by distance. Negative charges subtract from the total. The multiple charge option accepts charge and distance pairs. This helps study charge arrays quickly. Use commas between pairs. Use semicolons for cleaner long entries.
Advanced Use Cases
The page supports point potential, pair energy, work based potential, voltage based energy, potential difference energy, and capacitor energy. These modes cover many electrostatics problems. They also help compare homework answers with unit converted values. Always check charge units before submitting. A microcoulomb mistake changes results by one million. Compare joules with electronvolts for particle work. Compare volts with kilovolts for equipment estimates.
Reading The Output
The result panel shows the main answer first. It also lists standard SI values. Extra notes explain signs and assumptions. Export buttons save the same calculation for reports. Use the example table to test known inputs. Rounded values are shown for quick reading. Scientific notation preserves very large or tiny results. Keep raw inputs available when reviewing classroom or laboratory solutions later with peers. Careful inputs make every electrostatic result more reliable today.
FAQs
What is electric potential?
Electric potential is electric potential energy per unit charge. It measures how much energy each coulomb has at a point in an electric field.
What is electric potential energy?
Electric potential energy is stored energy caused by charge positions. It depends on charges, separation, medium, and chosen reference point.
Why can potential energy be negative?
Negative potential energy usually means attraction. Opposite charges lower system energy as they move closer together.
Why can electric potential be negative?
Potential becomes negative near negative source charges. The sign tells how a positive test charge would change energy.
Which distance should I enter?
Enter the center to center separation for point charge models. For extended bodies, use a model matching the actual geometry.
What is relative permittivity?
Relative permittivity compares a material with vacuum. Higher values reduce electric interaction strength in this simplified model.
Can I use this for electronvolt results?
Yes. Choose eV or MeV as the output energy unit. This is helpful for particle and atomic scale work.
How do multiple charges combine?
Electric potential is scalar. Add each signed contribution directly. Direction is not needed for potential sums.
Does the calculator include electric field direction?
No. It focuses on potential and energy. Electric field calculations require vector direction and component handling.
Can this handle capacitor energy?
Yes. Select capacitor mode. Enter capacitance and voltage. The calculator uses one half times capacitance times voltage squared.
Are exported results exact?
Exports use the displayed rounded values. Keep original inputs for precise recalculation and reports later.