Physics and engineering
Electric Field Solver Calculator
Superpose two signed point-charge field vectors at a 2D probe, then compute scalar potential, test-charge force, and test potential energy.
CURRENT MODEL
Place two source charges and one field probe
Physics students, electrostatics laboratory teams, and early-stage designers checking field direction and cancellation between two localized charges.
Decision supportedLocate the resultant field vector and potential at one probe point before selecting a test charge, sensor orientation, or safer measurement location.
LIVE FIELD VECTORS
Two-source vector superposition
The live coordinate view places both charges and the probe from current inputs, then points each normalized contribution in its calculated direction.
| Quantity | Symbol or equation | Current value | Unit |
|---|
How to use
Build the resultant from signed source contributions
- Enter each source charge with its physical sign in microcoulombs.
- Place both sources on the x-axis using signed centimetre coordinates.
- Enter the probe's signed x and y coordinates without placing it on a source.
- Add a signed test charge only if force direction or potential energy is needed.
- Read Ex and Ey before interpreting magnitude and direction; cancellation can make angle undefined.
- Retain individual source distances and vectors so the superposition can be independently checked.
Electric-field fundamentals
Six rules prevent scalar and vector quantities from being mixed
- Positive-source direction
- Field points away from a positive point charge at the probe.
- Negative-source direction
- Field points toward a negative point charge at the probe.
- Inverse-square magnitude
- Each field magnitude scales as |q|/r squared.
- Vector superposition
- Ex and Ey add component by component before magnitude is calculated.
- Scalar potential
- Signed kq/r contributions add algebraically without a direction.
- Test-charge independence
- An ideal infinitesimal test charge samples but does not alter the source field.
Calculation method
Convert coordinates, solve each source, then combine unlike outputs correctly
Microcoulombs and centimetres are converted to SI before distance and inverse-cube vector scaling. Each displacement vector points from source to probe; the sign of q then determines whether the resulting contribution follows or opposes that displacement.
Field components are summed as vectors. Potential is summed separately as a scalar. The test charge multiplies the completed field for force and the completed potential for potential energy.
Cancellation is not zero potential
Equal positive charges cancel their midpoint field because directions oppose, while their positive scalar potentials reinforce.
Near-source conditioning
Because field scales with inverse distance squared, coordinate uncertainty near a source can dominate the output and should be propagated rather than rounded away.
Probe disturbance
A real probe has finite size and can polarize or redistribute nearby charge. The ideal test-charge assumption is best far from conductive boundaries.
Detailed calculation process
Symbols, current substitution, intermediate quantities, and reconciliation
E = sum[k q_i r_i/r_i^3]; V = sum[k q_i/r_i]; F_t = q_t E; U_t = q_t VCharge and coordinate conversions, individual vectors, sums, magnitude, and potential retain full precision. Direction is omitted at vector cancellation before formatting.
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| q1 | First signed source charge | +2 | microC |
| q2 | Second signed source charge | -1 | microC |
| r_i | Source-to-probe displacement | calculated | m |
| E | Resultant field vector | calculated | V/m |
| V | Scalar electric potential | calculated | V |
| q_t | Signed test charge | +1 | nC |
Waiting for valid inputs.
Interpretation
Use components for orientation and potential for energetic comparison
The field angle reports the direction a positive test charge would accelerate. A negative test charge accelerates oppositely. Potential can remain large where the vector field cancels, so sensor force and discharge-energy questions must not substitute one output for the other.
Evidence and measurement
Preserve charge geometry and environmental assumptions
Record source construction and charge estimate, coordinate datum, probe location and dimensions, humidity and surrounding dielectric, conductor boundaries, grounding state, test-charge sign, instrument bandwidth, uncertainty, and whether charges remained stationary during measurement.
Scope and limitations
Where the point-charge vacuum model stops
- Finite conductors, charge redistribution, images, and grounded boundaries
- Dielectric polarization, interfaces, anisotropy, and nonlinear response
- Time-varying fields, radiation, magnetic force, and retardation
- Probe loading, finite sensor volume, and spatial averaging
- Air ionization, corona, breakdown, or discharge paths
- Electrical safety or insulation-system certification
Two stationary point charges in vacuum, positioned on the x-axis, with an observation point in the x-y plane. Superposition is electrostatic; finite conductor size, dielectric boundaries, and induction are excluded.
Key terminology
Electrostatic solver glossary
- Point charge
- Ideal source whose physical extent is negligible relative to distance.
- Electric field
- Force vector per unit positive test charge.
- Electric potential
- Scalar potential energy per unit charge.
- Superposition
- Linear addition of independent source contributions.
- Cancellation point
- Location where field vectors sum to zero.
- Coulomb constant
- SI proportionality 1/(4 pi epsilon0) for vacuum point charges.
Practical cases
Two probe locations with different physical meaning
Opposite-charge probe
At the default probe, unequal signed sources produce a 3.124468 MV/m resultant at 33.499657 degrees and 140.272100 kV potential. Both vector and scalar outputs matter.
Symmetric positive midpoint
Equal positive charges at -5 cm and +5 cm cancel the field at the origin. The angle is undefined, yet potential remains positive and a moved charge can still exchange energy.
Important note
Ideal source math is not high-voltage clearance approval
Use the solver for electrostatic reasoning and cross-checks. Real insulation and exposure decisions require conductor geometry, material, environment, transient, and breakdown evidence.
Frequently asked questions
Why are electric fields added as vectors?
Each charge produces a direction and magnitude at the probe. Components must be summed before computing the resultant magnitude and angle.
Why is electric potential added as a scalar?
Potential is energy per unit charge and has no spatial direction. Signed contributions therefore add algebraically even when field vectors point differently.
Can the field be zero while potential is not zero?
Yes. Equal positive charges at their midpoint cancel field vectors but add positive potential. Field cancellation does not imply zero potential.
What happens for a negative test charge?
Its force direction is opposite the electric field and its potential energy qV changes sign. The source field itself is unchanged.
Why can the probe not sit on a point charge?
The ideal point-charge expressions divide by r squared or r. At r=0 the ideal model is singular and cannot return a finite physical result.
Can this model conductors or dielectric interfaces?
No. Conductors redistribute charge and dielectrics polarize, altering boundary conditions. Those cases need geometry-aware numerical field analysis or an analytic boundary solution.
Authority and follow-on work
Reliable sources and related calculators
- OpenStax University Physics — Electric FieldSupports point-charge fields, direction, force definition, and vector superposition.
- OpenStax Physics — Electric PotentialSupports scalar electric potential and algebraic superposition.
- NIST CODATA — Fundamental ConstantsProvides vacuum permittivity used to derive Coulomb's constant.
Related calculators
Continue with a distinct physics question without silently changing the model boundary.