Coulomb's Law Calculator

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Overview

Coulomb's Law quantifies the force of attraction or repulsion between two electrically charged particles. It states that the magnitude of the electrostatic force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The constant of proportionality, k, is Coulomb's constant, which depends on the medium. This fundamental law is crucial for understanding electric fields, potential, and the behavior of charged particles in various physical systems.

Symbols

Variables

k = Coulomb's Constant, q_1 = Charge 1, q_2 = Charge 2, r = Distance between charges, F = Electrostatic Force

Apply it well

When To Use

When to use: Apply this formula when you need to determine the electrostatic force between two point charges, given their magnitudes and the distance separating them. It's also used to find an unknown charge or distance if the force and other variables are known. Ensure charges are in Coulombs and distance in meters.

Why it matters: Coulomb's Law is foundational to electromagnetism, explaining phenomena from atomic structure to the operation of electronic devices. It's essential for understanding how charges interact, forming the basis for electric circuits, capacitors, and the behavior of matter at a microscopic level. Its principles are applied in fields like materials science, particle physics, and electrical engineering.

Avoid these traps

Common Mistakes

• Forgetting to square the distance 'r'.
• Not using the absolute value for charges, leading to negative force magnitudes (which is incorrect for magnitude).
• Mixing units (e.g., cm for distance instead of m, microcoulombs instead of Coulombs without conversion).
• Confusing Coulomb's Law with Newton's Law of Universal Gravitation (similar inverse square relationship but different forces and constants).

One free problem

Practice Problem

Two point charges, $q_1=2.0\mu C$ and $q_2=3.0\mu C$, are separated by a distance of $5.0$ cm. Calculate the magnitude of the electrostatic force between them in a vacuum. Use Coulomb's constant $k=8.987\times 10^9{\text{ N m}}^2/{\text{C}}^2$. Round to two decimal places.

Solve for: $F$

Hint: Remember to convert microcoulombs to coulombs and centimeters to meters.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. Halliday, Resnick, Walker, Fundamentals of Physics
2. Griffiths, Introduction to Electrodynamics
3. Wikipedia: Coulomb's law
4. Encyclopædia Britannica: Coulomb's law
5. NIST CODATA (for k in SI)
6. Fundamentals of Physics by Halliday, Resnick, and Walker
7. Introduction to Electrodynamics by David J. Griffiths
8. Coulomb's law (Wikipedia article title)