Coulomb's Law Calculator
Calculate the electrostatic force between two point charges.
Understanding Coulomb's Law Calculator
Coulomb's Law: the force between two point charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance.
$$F = k\frac{|q_1 q_2|}{r^2}$$
How to use this calculator
- Enter the first charge, using coulombs, as the value of \(q_1\).
- Enter the second charge, using coulombs, as the value of \(q_2\).
- Enter the distance between the charges, using meters, as \(r\).
- Click calculate to find the force \(F\) in newtons.
The formula explained
The formula \(F = k\frac{|q_1 q_2|}{r^2}\) computes the magnitude of the electrostatic force between two point charges. The constant \(k\) is Coulomb's constant, and the absolute value makes the force size positive.
- F = magnitude of the electrostatic force, in newtons
- k = Coulomb's constant, approximately \(8.99 \times 10^9\,\text{N}\cdot\text{m}^2/\text{C}^2\)
- \(q_1\) = first charge, in coulombs
- \(q_2\) = second charge, in coulombs
- r = distance between the two charges, in meters
Step by step method
- Write down \(q_1\), \(q_2\), and \(r\) with the correct units.
- Multiply the charges, take the absolute value, then multiply by \(k\).
- Square the distance \(r\), then divide by \(r^2\).
- State the result as the force magnitude in newtons. If the charges have the same sign, they repel, and if they have opposite signs, they attract.
Worked example
Problem. Find the electrostatic force between \(q_1 = 2.0 \times 10^{-6}\,\text{C}\) and \(q_2 = -3.0 \times 10^{-6}\,\text{C}\) when the distance between them is \(r = 0.50\,\text{m}\).
- Use Coulomb's law: \(F = k\frac{|q_1 q_2|}{r^2}\).
- Substitute the values: \(F = 8.99 \times 10^9 \cdot \frac{|(2.0 \times 10^{-6})(-3.0 \times 10^{-6})|}{(0.50)^2}\).
- Compute the result: \(F = 8.99 \times 10^9 \cdot \frac{6.0 \times 10^{-12}}{0.25} = 0.21576\,\text{N}\), so the force is about \(0.216\,\text{N}\).
Answer. \(0.216\,\text{N}\), attractive
Tips and common mistakes
- Keep all charges in coulombs and the distance in meters, or the result will be wrong.
- This formula gives force magnitude only, so use the signs of the charges to decide whether the force is attractive or repulsive.
Frequently asked questions
How do I use a Coulomb's law calculator?+
Enter the two charges, q1 and q2, in coulombs, then enter the distance r between them in meters. The calculator uses F = k|q1 q2|/r^2 to find the magnitude of the electrostatic force.
What does the Coulomb's law formula mean?+
The formula shows that electric force gets stronger when either charge gets larger and weaker when the distance between them increases. The constant k is Coulomb's constant, about 8.99 × 10^9 N·m^2/C^2.
What units should I use for charges and distance?+
Use coulombs for charge and meters for distance, because the force comes out in newtons when those SI units are used. If your values are in microcoulombs or centimeters, convert them first.
Does the calculator tell me whether the force is attractive or repulsive?+
The formula shown uses absolute values, so it gives the force magnitude only. To determine the direction, remember that like charges repel and opposite charges attract.
What happens if one charge is zero or the distance is very small?+
If one charge is zero, the force is zero. If the distance is very small, the force becomes very large because the force varies with 1/r^2, so careful unit conversion matters.
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