Calculator
Formula Used
General formula: ΔV = -∫ E · dl
Uniform field: ΔV = -E d cosθ
Vector field: ΔV = -(ExΔx + EyΔy + EzΔz)
Radial field: ΔV = E0 r0²(1/rb - 1/ra)
Sampled field: ΔV ≈ -Σ(Ei Δli)
Final potential: Vfinal = Vreference + ΔV
Energy change: ΔU = qΔV
How to Use This Calculator
Select the method that matches your field model.
Use the uniform option when field strength is constant.
Use vector mode when field and displacement have components.
Use radial mode for inverse square electric fields.
Use sampled mode for measured or simulated field segments.
Enter a reference potential if the starting voltage is known.
Enter charge when you also need energy and field work.
Press calculate. The result appears above the form.
Example Data Table
| Case | Method | Input Summary | Formula | Expected Result |
|---|---|---|---|---|
| Plate gap | Uniform | E = 500 V/m, d = 0.2 m, θ = 0° | ΔV = -E d cosθ | ΔV = -100 V |
| Angled path | Uniform | E = 800 V/m, d = 0.1 m, θ = 60° | ΔV = -E d cosθ | ΔV = -40 V |
| Component move | Vector | Ex = 120, Ey = 40, Δx = 0.15, Δy = 0.05 | ΔV = -(ExΔx + EyΔy) | ΔV = -20 V |
| Radial source | Radial | E0 = 900 V/m, r0 = 0.1 m, ra = 0.1 m, rb = 0.3 m | ΔV = E0r0²(1/rb - 1/ra) | ΔV = -60 V |
Article
What Electric Potential Means
Electric potential describes voltage at a point. It links field strength with position. A strong field can create a large voltage change over a short path. A weak field can still matter when distance is long. This calculator focuses on that relationship.
Why the Sign Matters
The main idea is a line integral. Electric field points in the direction that positive charge is pushed. Potential falls when you move with the field. Potential rises when you move against it. The negative sign in the formula shows this rule.
Uniform Field Work
Many practical tasks use a uniform field estimate. Air gaps, plates, insulation layers, and test fixtures often begin with that model. Enter field strength, path length, and angle. The tool finds the component of the field along the path. That component sets the voltage change.
Vector Field Work
Vector work needs components. When the field has x, y, and z values, each part can contribute. The dot product combines field components with displacement components. This is useful for simulations, cable spacing checks, and electrostatic design notes.
Radial Field Work
Radial fields need another model. If the field follows an inverse square pattern, distance from the source matters strongly. The voltage change between two radii is not simply field times distance. The calculator integrates the field using the chosen reference radius.
Sampled Path Work
Sampled path data helps with measured or simulated points. You can enter field and step pairs. The calculator sums each local contribution. This gives a practical approximation when the field is not constant. Smaller steps usually improve accuracy.
Units and Energy
Units also affect clarity. Field values may be entered as volts per meter, kilovolts per meter, or volts per centimeter. Distances may use meters, centimeters, or millimeters. The result can be shown in volts, millivolts, or kilovolts.
Charge and Work
Use the charge field when energy is needed. Potential is energy per charge. Multiplying voltage change by charge gives electric potential energy change. The work done by the electric field has the opposite sign.
Result Review
Always review signs. A negative voltage change does not mean an error. It often means the path follows the electric field. Check angle, direction, and reference voltage before using the result.
Exporting Results
For reports, export the calculation. The CSV suits spreadsheets. The PDF gives a compact record for checks, notes, teaching, and later review.
FAQs
What does electric potential from field mean?
It means finding voltage change from electric field strength along a path. The calculation uses the negative line integral of the field over distance.
Why is there a negative sign?
Potential drops when movement follows the electric field. It rises when movement goes against the field. The negative sign captures that direction rule.
When should I use uniform field mode?
Use it when the field is nearly constant. It is useful for parallel plates, short insulation gaps, and simple electrical estimates.
When should I use vector component mode?
Use it when the electric field and movement have x, y, and z components. The calculator applies the dot product.
What does radial mode calculate?
It estimates voltage change for an inverse square field. This is useful when field strength changes with distance from a source.
How should sampled data be entered?
Enter one field and step pair per line. Use a comma between them. Example: 120,0.02.
Can this calculator find energy?
Yes. Enter charge in coulombs. The calculator multiplies charge by potential change to find potential energy change.
Why is my voltage change negative?
A negative value usually means your path follows the electric field direction. Check the angle, component signs, and reference point.