Enter Charge, Distance, and Medium Values
Coulomb Law Formula
F = (1 / 4πε) × |q1q2| / r²
F = (k / εr) × |q1q2| / r²
Here, F is force in newtons, q1 and q2 are charges in coulombs, r is separation in meters, k is 8.9875517923 × 10⁹ N·m²/C², εr is relative permittivity, and ε is absolute permittivity.
How to Use This Calculator
- Enter both charges with their correct signs and units.
- Choose distance mode or 3D coordinate mode.
- Enter separation distance, or enter both charge positions.
- Select a medium preset, or choose a custom relative permittivity.
- Select the desired force output unit.
- Press the calculate button to view force, components, field, and energy.
Example Data Table
| Case | q1 | q2 | r | Medium | Force direction | Approximate force |
|---|---|---|---|---|---|---|
| Small lab charges | 5 μC | -3 μC | 0.25 m | Air | Attractive | 2.16 N |
| Two positive charges | 2 nC | 7 nC | 4 cm | Vacuum | Repulsive | 7.86e-5 N |
| Water medium | 1 μC | 1 μC | 0.10 m | Water | Repulsive | 0.0112 N |
Understanding Electrostatic Force
Electrostatic force is the push or pull between electric charges at rest. It is a central idea in classical physics. The force follows an inverse square law. This means distance has a very strong effect. If the distance doubles, the force becomes one fourth. If the distance halves, the force becomes four times larger.
Coulomb law links force, charge size, spacing, and medium. Larger charges create a stronger interaction. Smaller spacing also creates a stronger interaction. The sign of each charge controls the direction. Two positive charges repel. Two negative charges also repel. One positive charge and one negative charge attract each other.
The medium between charges matters. Vacuum gives the reference value of Coulomb constant. Air is almost the same for many school and lab problems. Water, glass, paper, and other dielectrics can reduce the force. They do this because bound charges inside the material respond to the electric field. This response weakens the direct interaction between the two free charges.
This calculator uses standard unit conversions before applying the formula. That prevents common mistakes with microcoulombs, nanocoulombs, centimeters, and millimeters. It also accepts electron charge units. That option is useful in atomic and semiconductor problems. The coordinate mode is useful for three dimensional problems. It finds the separation from two positions. It then resolves force into x, y, and z components.
Force magnitude is always shown as a positive size. Signed force keeps charge direction information. A positive signed value indicates repulsion along the selected direction vector. A negative signed value indicates attraction opposite that vector. The vector components follow the same sign convention. This helps when the electrostatic force must be combined with other forces.
The calculator also reports electric field, potential, and potential energy. The electric field value is the field from q1 at the position of q2. Potential energy shows whether the charge pair has positive or negative stored energy. These extra outputs help with circuits, charged particles, molecular models, and field mapping tasks.
Use measured values carefully. Electrostatic experiments can be sensitive to humidity, leakage paths, nearby conductors, and charge distribution. Coulomb law assumes point charges or spherical charges at distances much larger than their radii. For extended bodies, the result is an estimate unless symmetry makes the point charge model valid.
Always check the distance first. A zero distance is not physical for point charge calculations. Very small distances can create very large forces. In real materials, quantum effects, surface contact, breakdown, and charge spreading can limit simple classical predictions.
For classroom work, keep all values in scientific notation. It makes very small charges easier to compare. For design work, use conservative spacing. Nearby metal surfaces can change field lines. Insulators can hold stray charge. Measurement tools can also disturb weak fields. Recheck polarity before interpreting attraction. Recheck units before trusting any final force value in every lab report and design note carefully.
FAQs
What is electrostatic force?
Electrostatic force is the attractive or repulsive force between electric charges at rest. It acts along the line joining the charges. Its strength depends on charge sizes, distance, and the medium between them.
Which formula does this calculator use?
It uses Coulomb law: F = (k / εr) × |q1q2| / r². The calculator converts entered units first, then computes force in newtons or the selected output unit.
Why does distance have a squared term?
Electric influence spreads through space. For point charges, that spreading follows an inverse square pattern. Doubling distance reduces force to one fourth. Tripling distance reduces force to one ninth.
Should charges be entered with signs?
Yes. Use positive values for positive charges and negative values for negative charges. The signs help identify attraction or repulsion and give meaningful signed vector components.
What is relative permittivity?
Relative permittivity, written as εr, compares a material with vacuum. A larger εr usually lowers the electrostatic force. Air is close to one, while water is much larger.
Can I use centimeters or microcoulombs?
Yes. The form accepts common charge and distance units. It converts them into coulombs and meters internally before applying Coulomb law, so the final result stays consistent.
What does the signed force mean?
A positive signed force means repulsion along the chosen direction. A negative signed force means attraction opposite that direction. The magnitude stays positive because it only represents force size.
When should I use coordinate mode?
Use coordinate mode when the two charges are given by positions in space. The calculator finds the 3D separation automatically and returns x, y, and z force components.
Does this work for large charged objects?
It works best for point charges or spherical charges when distance is large compared with size. For irregular extended bodies, the result is an approximation unless charge distribution is known.
Why is force lower in water?
Water has a high relative permittivity. Its molecules respond strongly to electric fields. That response screens the interaction between charges and lowers the effective force predicted by Coulomb law.
Can force become infinite?
The point charge formula grows without limit as distance approaches zero. Real charges are not perfect mathematical points. At tiny scales, contact effects and quantum behavior limit the simple model.