Nearest Neighbor Coulombic Repulsion Calculator

Estimate Coulombic repulsion for adjacent charged particles. Adjust charge, distance, dielectric, lattice type, and spacing. Get clear steps, tables, exports, and study ready answers.

Calculator Form

Formula Used

The calculator uses Coulomb law with dielectric correction.

F = k × |q₁q₂| ÷ (εᵣ × r²)

Here, F is force in newtons. The constant k is 8.9875517923 × 10⁹ N·m²/C². The terms q₁ and q₂ are charges in coulombs. The term r is nearest neighbor distance in meters. The term εᵣ is relative permittivity.

Potential energy is also calculated as U = kq₁q₂ ÷ (εᵣr).

How to Use This Calculator

  1. Enter both nearest neighbor charges.
  2. Choose the correct charge units.
  3. Select direct spacing or lattice based spacing.
  4. Enter distance or lattice parameter.
  5. Pick a medium or enter custom relative permittivity.
  6. Add coordination number when needed.
  7. Press the calculate button.
  8. Download the result as CSV or PDF.

Example Data Table

Case q₁ q₂ Distance Medium Approximate Force
Two singly charged ions +1 e +1 e 0.30 nm Vacuum 2.56e-9 N
Same ions in water +1 e +1 e 0.30 nm Water 3.27e-11 N
Divalent and monovalent ions +2 e +1 e 0.25 nm Vacuum 7.38e-9 N

Nearest Neighbor Repulsion Guide

Coulombic repulsion describes the push between two charges with the same sign. In a crystal, polymer, plasma, or molecular model, the nearest neighbor spacing often controls the largest pair force. This calculator focuses on that closest pair. It accepts direct separation or a lattice parameter. It also adjusts the result for a surrounding dielectric medium.

Why The Distance Matters

The force changes with the inverse square of distance. A small spacing change can create a large force change. This is why angstrom and nanometer inputs are useful for atomic problems. The tool converts every distance to meters before applying the formula. It can also find nearest neighbor distance from common cubic structures.

Charge And Medium Choices

Charge may be entered in coulombs or as elementary charge units. Elementary charge input is practical for ions. For example, sodium ion charge is +1 e. Chloride ion charge is -1 e. When both signs match, the interaction is repulsive. When signs differ, the magnitude is still shown, but the interaction is attractive.

The dielectric setting divides the vacuum force by relative permittivity. Vacuum keeps the force unchanged. Water greatly reduces charge interaction. Custom relative permittivity helps with solids, solvents, and teaching examples. Use a value greater than zero.

Lattice Interpretation

Nearest neighbor distance depends on geometry. Simple cubic uses the lattice parameter directly. Body centered cubic uses the body diagonal half distance. Face centered cubic uses the face diagonal neighbor distance. Diamond cubic uses one quarter of the body diagonal. These options prevent common spacing mistakes.

Using The Results

The main force result is the pairwise magnitude in newtons. Extra units help readability. The signed force marker explains whether the pair is repulsive or attractive. Potential energy is also displayed. A coordination number can estimate the scalar sum for all nearest neighbors around one particle. That sum is not a net vector force in a perfect symmetric lattice. It is a comparison value.

Good Practice

Use measured spacing when possible. Match charge signs carefully. Select the medium that best represents the environment. For high precision work, confirm lattice type, temperature, screening, and quantum effects. Classical Coulomb law is powerful, but real materials can need additional models and validation checks.

FAQs

What is nearest neighbor Coulombic repulsion?

It is the electric pushing force between the closest two particles that carry charges with the same sign.

Which formula does this calculator use?

It uses Coulomb law. The force equals k times the charge product divided by relative permittivity and distance squared.

Can I use elementary charge units?

Yes. Select elementary charge as the unit. Then enter values like 1, 2, or -1 for ionic charge states.

What happens when charges have opposite signs?

The calculator still shows the force magnitude. It also marks the interaction as attractive instead of repulsive.

Why does relative permittivity matter?

A medium weakens the electric force. Higher relative permittivity gives a smaller force for the same charges and spacing.

What is coordination number?

Coordination number is the count of nearest neighbors around one particle. It helps estimate a scalar total interaction budget.

Is the scalar neighbor sum a net force?

No. In symmetric crystals, vector forces may cancel. The scalar sum is only a comparison measure.

Can this replace advanced material modeling?

No. It gives a classical pairwise estimate. Real materials may need screening, bonding, temperature, and quantum corrections.

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