Coulomb's Law

The question this electrostatic model answers

The calculator answers one defined question: what force magnitude follows from two supplied point charges and a supplied separation under Coulomb's law? It validates the signed charge values, takes the absolute value of their product for magnitude, divides by squared distance, and uses the fixed constant. It does not measure charge, locate an object, or infer whether the point-charge approximation is appropriate.

The signs are retained for one additional conclusion. Opposite nonzero signs indicate attraction, while like nonzero signs indicate repulsion. A zero charge gives zero force and is not described as either attraction or repulsion. This sign interpretation is part of the elementary relation; it is not electrical safety advice or a circuit behavior prediction.

• Inputs are two signed charges and separation.
• Output is force magnitude in newtons.
• Signs identify attraction or repulsion.
• Scope is point-charge electrostatics only.

What a point charge means

The point-charge idealization treats all charge as concentrated at one location. Separation r is then the distance between those two locations, and the field has spherical symmetry around each isolated source in the simple vacuum relation. The calculator accepts the point-charge premise rather than deriving it from shape, size, conductor geometry, or charge density.

An extended charged object can have charge spread across a surface or volume, and different portions may be at different distances. Its force on another object can require integration or a symmetry argument. Nearby conductors and dielectric materials can also redistribute or polarize charge. Those effects are outside the three-field contract and must not be assumed to have been included.

• Charge is concentrated at an ideal point.
• Separation is between point locations.
• Charge distribution is not modeled.
• Nearby material response is excluded.

Signed charge values

Each charge field accepts a signed value from -1,000,000 C through 1,000,000 C. The sign represents the elementary charge polarity convention. For the magnitude calculation, the product is placed inside absolute-value bars, so reversing one sign changes the relationship from like to unlike without changing the magnitude when absolute values stay the same.

A zero charge is valid and makes the product zero. The handler reports zero force and describes the sign relationship as zero force for a zero charge rather than forcing an attraction or repulsion label. This explicit case keeps the text result faithful to the input. It does not describe neutral-object polarization or induced forces, which are not represented.

• Charges may be positive, negative, or zero.
• Magnitude uses absolute q1 q2.
• Opposite signs attract in the model.
• Like nonzero signs repel in the model.

Separation and inverse-square behavior

Separation r is a positive distance in metres and appears squared in the denominator. Doubling the distance reduces the magnitude to one quarter, while halving it increases the magnitude by four. This inverse-square behavior is a central feature of the point-charge relation. A zero separation is rejected because the formula would be singular and the two point locations would coincide.

The supported separation range is 0.000001 m through 1,000,000,000 m. The endpoints are computational limits and do not assert that point charges or classical electrostatics are valid at every scale. The handler applies the formula to the entered distance and does not replace it with a finite-size or short-range correction.

• Separation is strictly positive.
• Force varies as 1/r^2.
• Doubling distance gives one quarter magnitude.
• Zero distance is rejected.

The Coulomb constant

The handler uses k = 8.9875517923e9 N m^2/C^2. This constant connects coulomb charges and metre separation to newtons in the stated ideal relation. Keeping the value explicit makes known answers reproducible and avoids an unrecorded rounding choice. The constant is fixed by the calculator contract rather than entered as a third physical assumption.

The constant does not describe a circuit's resistance, voltage source, or electrical power. It sets the force scale for the point-charge law. Material permittivity can alter electrostatic interactions in a medium, but this page does not ask for a medium or use a dielectric correction.

• k is fixed at 8.9875517923e9.
• Its unit is N m^2/C^2.
• k is not a circuit parameter.
• No dielectric correction is used.

The formula and unit path

The magnitude formula is F = k |q1 q2| / r^2. The units are N m^2/C^2 multiplied by C squared and divided by m squared, leaving N. The absolute value removes the sign from the magnitude while the separate sign check supplies the attraction or repulsion wording. This separation of magnitude and relationship makes the output easy to audit.

The formula is the point-charge textbook boundary of the page. It does not add vector direction, a field from multiple charges, induced charge, dielectric polarization, circuit current, or time variation. A more detailed electrostatic problem requires a defined geometry and material context rather than an implicit correction to this product.

• F = k |q1 q2| / r^2.
• Unit cancellation leaves newtons.
• Absolute value supplies magnitude.
• Signs supply relationship text.

An opposite-sign example

Use q1 = 1e-6 C, q2 = -1e-6 C, and r = 1 m. The absolute charge product is 1e-12 C^2. Multiplying by k gives 0.0089875517923 N after the one-metre denominator is applied. Because the signs are opposite, the calculator says the charges attract. The numerical result and text relationship come from the same validated input set.

This example is a calibration of the fixed constant and sign branch. It does not specify a physical capacitor, wire, electrode, or operating voltage, and it does not tell a user how to handle charged objects. The intended conclusion is only the point-charge force magnitude and attraction label.

• First charge: 1e-6 C.
• Second charge: -1e-6 C.
• Force magnitude: 0.0089875517923 N.
• Relationship: attraction.

Like signs and zero charge

If both charges are positive or both are negative, their product is positive and the ideal point-charge relationship is repulsion. For example, changing the second charge in the catalog example from -1e-6 C to +1e-6 C leaves the magnitude unchanged but changes the text from attraction to repulsion. The handler therefore checks signs separately from the absolute-value arithmetic.

If either charge is zero, the force magnitude is zero. The output text identifies that zero-charge case rather than calling it attractive or repulsive. Real neutral objects can still interact through induced effects in some situations, but those mechanisms are not part of this point-charge contract.

• Like positive charges repel.
• Like negative charges repel.
• Zero charge gives zero model force.
• Induced neutral-object effects are excluded.

Scaling checks

The magnitude is linear in the absolute value of each charge and inverse-square in separation. Doubling one charge doubles force; doubling both charges quadruples it. Doubling separation divides the result by four. These relationships are useful for checking a worksheet and for catching an accidental missing square or absolute value.

Scaling comparisons need a common point-charge and medium assumption. Changing the charge distribution or placing the charges near a conductor can change the actual field. The handler cannot detect those changes, so the algebraic scaling should be interpreted as a property of the selected ideal formula, not as universal equipment behavior.

• Magnitude is linear in each charge magnitude.
• Distance enters as an inverse square.
• The sign branch does not alter magnitude.
• Scaling is an ideal-model check.

Force magnitude versus vector force

The full electric force has direction along the line joining the charges, with the sign relationship determining whether the direction points toward or away from the other charge. This page returns a scalar magnitude and the words attraction or repulsion. It does not return a coordinate vector because no positions or coordinate system are fields.

For multiple charges, forces add as vectors and can cancel or reinforce. A single pair magnitude cannot be used as the net force without checking all other interactions. The output should retain its label as the two-point-charge magnitude and should not be silently promoted to a system-level force.

• The output is scalar magnitude.
• Attraction and repulsion give direction words only.
• No coordinate vector is returned.
• Multiple charges need vector addition.

Validation and finite guards

The handler requires finite JavaScript charge numbers within the signed bounds and a finite positive separation within its range. Numeric strings, missing values, NaN, infinities, zero separation, and out-of-range values are rejected. This direct validation protects the pure function when called without the form and keeps the division and product paths explicit.

The absolute product, inverse-square result, and result entry receive finite checks. The engine does not clip a charge, replace a zero distance, or evaluate text as an expression. An error is preferable to a plausible force produced from a silently altered electrostatic scenario.

• Charges must be finite signed numbers.
• Separation must be finite and positive.
• Magnitude and result are guarded.
• Invalid values are rejected rather than changed.

Material and circuit effects outside scope

A real electrostatic setup may include conductors, insulators, grounded surfaces, image charges, dielectric response, charge leakage, and a spatially varying distribution. A circuit adds voltage, current, capacitance, resistance, switching, and time. None of those facts is represented by two point charges and one distance. The calculator does not infer them from the units or signs.

This omission is the requested model boundary, not a claim that those effects are unimportant. Use the result as a point-charge textbook term or teaching value. If a system analysis needs field maps, induced charge, or circuit behavior, define that separate model and preserve the present result only where its assumptions remain valid.

• Conductors and dielectric response are absent.
• No circuit variables are entered.
• No field map is calculated.
• The point-charge boundary remains explicit.

Explicit electrical safety boundary

The force number does not tell a user whether a charged object, electrode, cable, capacitor, or enclosure is safe. Safety can depend on voltage, energy, current path, insulation, clearance, environment, stored charge, and applicable procedures. Those variables are not in Coulomb's law as used here, and the calculator does not supply them.

The page therefore includes no electrical safety advice. This is important even when the output is finite and the sign branch is clear. A point-charge force calculation can support classroom reasoning, but it cannot authorize handling, construction, energization, or installation.

• Force is not a safety rating.
• Voltage and current are not modeled.
• Clearance and insulation are not assessed.
• No electrical safety advice is given.

A reproducible Coulomb report

A clear report records q1 and q2 with signs, defines separation, states k, and shows the absolute-value product and inverse-square denominator. It labels the numerical result as force magnitude in newtons and records attraction, repulsion, or zero force for a zero charge. The sign convention should remain visible because it changes the relationship branch.

End with the model boundary: point-charge Coulomb arithmetic only, with no circuit or electrical safety advice. This allows the number to be reused in a worksheet without suggesting that the page analyzed an apparatus or approved an operating condition.

• Record signed charge values.
• Record distance and k.
• Keep magnitude and sign relationship separate.
• Attach the no-safety-advice boundary.

Appropriate educational use

The calculator is useful for electrostatics lessons, inverse-square scaling, sign conventions, and dimensional analysis. It demonstrates that changing a charge sign can change attraction to repulsion without changing magnitude, and that changing separation has a squared effect. Its explicit zero branch is helpful when discussing neutral inputs and model assumptions.

It should not be used to design a circuit, select insulation, estimate a device rating, or issue an electrical procedure. When the question becomes operational, the point-charge result is at most one idealized input to a separate analysis.

• Good for Coulomb-law instruction.
• Good for sign and scaling checks.
• Not a circuit-design calculator.
• Not electrical safety advice.

Final interpretation checklist

Check that both charges are signed coulomb values, separation is a positive metre distance, and k is the specified constant. Confirm that the magnitude uses absolute charge product and squared separation, then check whether signs indicate attraction or repulsion. Test zero, like-sign, and opposite-sign examples. These checks verify the point-charge formula but not a real field geometry.

Then ask whether the desired conclusion is still a pairwise electrostatic magnitude. If it is, the result is transparent. If it asks about circuits, equipment, handling, clearance, or safety, stop at the boundary. F = k |q1 q2| / r^2 has been evaluated, with no electrical safety advice produced.

• Check signs, units, and distance.
• Check absolute value and inverse square.
• Check attraction or repulsion branch.
• Do not turn force arithmetic into safety guidance.

From electric field to force

Coulomb's pairwise force can be understood as a source charge creating an electric field and a second charge responding to that field. The current calculator combines both charges directly, so it returns mutual force magnitude in one step. It does not return the field of either charge separately and does not calculate potential or energy. Keeping those quantities distinct helps a learner select the correct equation for the question.

The second charge matters to force but not to the field produced by the first in the simplest point-charge description. A field calculation and a force calculation therefore have different input contracts even when both use the same constant. This page's two charge fields are intentional and should not be reduced to a single source-charge field without changing the model.

A full vector treatment also uses the line joining the charges. The magnitude and attraction or repulsion text provide the scalar information available from the current fields, but no coordinate components are returned.

• The page calculates pairwise force.
• A field and a force have different contracts.
• Both charges affect mutual force.
• No potential or field vector is returned.

Medium, proximity, and classical limits

The fixed Coulomb constant corresponds to the selected ideal electrostatic convention. In a material medium, effective permittivity can change the interaction, and nearby conductors can redistribute surface charge. The calculator has no medium or boundary fields, so it cannot apply those corrections. Its point-charge assumption is the complete geometry supplied to the handler.

At very small separations, charge size, quantum effects, contact, and material structure may matter more than a point-charge vacuum relation suggests. The lower bound prevents a singular zero distance but does not certify classical validity near that endpoint. The output should be read as the result of the mathematical contract.

At large scales, other fields and charges may be important. A pairwise magnitude can remain finite while failing to represent the net force in a real environment. The page does not claim isolation beyond the ideal pair premise.

• The constant assumes the chosen ideal convention.
• No dielectric or conductor correction is used.
• Small-distance validity is not certified.
• Other charges and fields are not summed.

Vector sums and careful reporting

For a set of charges, each pairwise force has a direction and the net force is the vector sum. Equal magnitudes can cancel or reinforce depending on geometry. The current calculator cannot answer that system question because it has no coordinates or additional charges. It can supply one pair contribution when its point-charge premises are appropriate.

A careful report records signs, separation definition, constant, and the attraction or repulsion branch. It should not attach a voltage, current, power, or safety label to a force number. The output precision reflects arithmetic representation, not the accuracy of a charge measurement or an environmental model.

When a larger electrical analysis uses the value, carry the point-charge assumption and the absence of material, circuit, and safety modeling forward. The cleanest handoff is a named pairwise force term rather than an unexplained system result.

• Net force requires vector addition.
• Keep sign relationship beside magnitude.
• Do not relabel force as voltage or power.
• Carry point-charge limits into larger analyses.

Charge measurement and sign records

A charge value can be measured, assigned in a classroom exercise, or inferred from another model. The calculator does not know which. Preserve the sign convention, measurement method, and whether the value is a net charge or an ideal point value outside the form. A number in coulombs supplies the arithmetic premise but not its experimental history.

Charge can also vary with time through leakage, transfer, or a changing circuit. The handler evaluates one fixed pair and has no time field. If a force changes, repeated calls can provide separate snapshots only when their time context is recorded; they do not create a dynamic simulation.

The attraction or repulsion text is based only on the supplied signs. It does not identify the path a real object will follow because other forces, constraints, and fields may be present.

• Record whether charges are measured or hypothetical.
• Preserve the sign convention.
• One fixed pair is evaluated.
• Sign text does not predict a path.

Superposition and field geometry

For several point charges, the electric field and force obey superposition: individual vector contributions are added. Two pairwise magnitudes can have equal values but point in different directions, so their net effect depends on coordinates. The current calculator has no coordinate fields and intentionally returns only one pair magnitude.

A charge near a conductor can induce a redistribution that changes the field from the isolated point-charge result. A dielectric can change the effective interaction through polarization. These are geometry and material questions, not hidden sign branches in the simple formula.

The page is therefore best used after the pairwise idealization has been chosen. If the environment is important, use a separate field or electrostatic model that owns the geometry and boundary conditions.

• Superposition is vector addition.
• Coordinates are absent.
• Conductors can alter charge distribution.
• Material boundaries need a separate model.

Safe and precise result handoff

The numerical result can be copied into a force balance or a lesson if its pairwise assumptions remain appropriate. Record the charges, separation, constant, magnitude, and sign relationship together. Do not strip the attraction or repulsion text because it explains how the signs were used.

A finite number is not evidence that a charged apparatus is safe. Voltage, stored energy, current path, insulation, clearances, environment, and procedures may dominate an actual electrical risk. None is represented by Coulomb's law as used here.

The honest handoff remains a point-charge force magnitude with no circuit or electrical safety advice. A larger analysis may add those questions, but it must not attribute them to this calculator.

• Keep magnitude and sign text together.
• A finite force is not a safety measure.
• Electrical context requires more variables.
• The page gives no safety advice.