Probe placement between like charges
Two positive calibration spheres of +4 nC and +9 nC separated by 0.5 m place the zero-field point 0.2 m from the smaller left source and 0.3 m from the right source.
Physics and electromagnetism
Electric Field Equilibrium Calculator
Find the finite point where two collinear point-charge electric fields cancel, identify its region, and audit the residual field and electric potential.
Two-source electrostatic balance
Locate a zero-field point without confusing it with zero potential
Place q1 at x = 0 and q2 at x = d. This calculator solves the one-dimensional vector cancellation problem, first selecting the physically possible region and then checking both signed field contributions at the reported coordinate.
Zero-field coordinate x-
Distance from q1-
Distance from q2-
Potential at x-
Current model evidence
Signed field-balance ledger
Use the region rule and signed residual together; a magnitude-only equality can select a mathematically wrong location.
| Step | Left-side basis | Right-side basis | Current value | Scope / unit |
|---|
DETAILED CALCULATION PROCESS
Formula, units, default substitution, and reconciliation
1. Governing relation
E(x) = k q1 sign(x)/x^2 + k q2 sign(x-d)/(x-d)^2 = 0
Choose the interval allowed by the charge signs, equate field magnitudes, solve the distance ratio, and then substitute the coordinate into the signed field equation. Same-sign charges cancel between them; opposite-sign unequal charges cancel outside the smaller-magnitude source.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| q1 | Signed source charge at x = 0 | C | +4 nC |
| q2 | Signed source charge at x = d | C | +9 nC |
| d | Source separation | m | 0.5 m |
| x | Coordinate measured from q1 | m | Solved |
| k | Coulomb constant | N m2/C2 | 8.9875517862e9 |
| V | Scalar electric potential at x | V | Computed independently |
3. Unit and sign normalization
- Each nanocoulomb input is multiplied by 1e-9 before Coulomb-law evaluation.
- The x-coordinate is signed: x < 0 is left of q1, 0 < x < d is between the charges, and x > d is right of q2.
- Charge signs determine field directions; absolute charge magnitudes enter the square-root distance ratio.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Five steps from measured inputs to a defensible result
- Assign the physical left source to q1 and measure all coordinates from its center.
- Enter signed charge values, preserving negative signs rather than entering magnitudes only.
- Enter the positive center-to-center separation in metres.
- Read the named region before using the coordinate in a drawing or apparatus layout.
- Confirm the signed residual is negligible and retain both distances because they catch coordinate-reference mistakes.
ELECTROMAGNETIC FOUNDATIONS
Concepts that control this specific model
- Electric field is a vector
- A field contribution has both magnitude and direction, so two equal magnitudes cancel only when their directions oppose.
- Superposition is component-wise
- The net field is the algebraic sum of each point-charge field along the common axis.
- Same signs cancel internally
- Between equal-sign charges the two fields point in opposite directions; outside they point together.
- Opposite signs cancel externally
- Between opposite signs both fields point from positive toward negative, so any zero must lie outside the pair.
- Zero field is not zero potential
- Potential adds as a signed scalar kq/r and can remain finite when vector fields cancel.
DEEP ANALYSIS 1
Why the smaller charge owns the outside zero
For opposite signs, the candidate must lie on the side of the smaller magnitude so its shorter distance can compensate for the stronger distant source.
DEEP ANALYSIS 2
Equal-and-opposite charges are a finite-point exception
Their outside fields approach equality only at infinity. The calculator rejects a finite answer instead of dividing by a vanishing distance-ratio denominator.
DEEP ANALYSIS 3
Equilibrium does not imply stable confinement
A test charge can have zero force at the reported point, but electrostatic fields alone do not create a stable three-dimensional free-space trap. This page only solves the axial cancellation.
RESULT INTERPRETATION
What the current output does and does not decide
The x-coordinate identifies a point in the chosen coordinate system, while r1 and r2 are geometry checks independent of left/right wording.
The potential result answers an energy-per-charge question and must not be used as evidence that the field equation was solved incorrectly.
REAL USE CASES
Two decisions with different boundary conditions
Opposite-charge external balance
For +4 nC at x = 0 and -9 nC at x = 0.5 m, cancellation occurs at x = -1 m, outside the smaller +4 nC source; no between-source solution exists.
EVIDENCE AND DATA QUALITY
What to retain with the exported result
Retain source-charge signs and uncertainty, center positions, separation measurement, coordinate-axis sketch, environmental geometry, and the exported signed E1/E2 residual. Nearby conductors or finite electrodes invalidate the point-source assumption.
LIMITS AND EXCLUSIONS
Where this physical model stops
- Models exactly two stationary point charges on one straight axis.
- Excludes conductor polarization, image charges, dielectric interfaces, shielding, and nearby charge distributions.
- Does not evaluate stability away from the axis or predict a trapped trajectory.
- Treats charge and separation as exact inputs and does not propagate measurement uncertainty.
- The point-charge equation is not valid at either source location.
TERMS USED HERE
Six terms that keep the calculation unambiguous
- Zero-field point
- Coordinate where the vector sum of modeled electric fields is zero.
- Superposition
- Linear addition of field contributions from separate sources.
- Coulomb constant
- Proportionality constant k in the vacuum point-charge field law.
- Signed coordinate
- Position retaining direction relative to a selected origin.
- Electric potential
- Scalar potential energy per unit test charge.
- Residual field
- Numerical signed sum used to verify cancellation after solving.
RELIABLE SOURCES
References supporting the equation and units
FREQUENTLY ASKED QUESTIONS
Questions specific to this calculation
Why is the answer between two positive charges?
Between like charges their fields oppose; outside the pair they point in the same direction and cannot cancel.
Why is an opposite-sign answer outside the charges?
Between opposite charges both fields point from positive to negative, so cancellation is possible only beyond one source.
Why are equal and opposite charges rejected?
Their axial field has no finite zero; the equality is approached only infinitely far away.
Can one source charge be zero?
No. That becomes a one-source problem with no finite zero-field point, so the input is rejected.
Does a zero field mean a test charge has zero potential energy?
No. Potential energy is q_test V, and V may be nonzero at a zero-field point.
Can I use centimetres for separation?
Convert them to metres first; the displayed separation field and all reported distances use metres.
IMPORTANT BOUNDARY
Use the result as analysis, not certification
This ideal two-point-charge result is an analytical screening value, not a high-voltage safety clearance, electrode design certification, or proof of stable particle confinement.