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Select the parameter (force, charge, or distance), and the calculator will determine its value in various units using Coulomb’s law.
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The online free Coulomb’s Law Calculator helps you determine the force of attraction or repulsion between two electric charges. It provides a step-by-step solution based on the magnitude of the charges and the distance between them.
“Coulomb’s Law states that the electrostatic force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.”
Coulomb’s Law explains how electrically charged particles interact. The electrostatic force acts along the straight line joining the two charges (q₁q₂) and depends inversely on the square of the separation distance (r²) between them.
The mathematical expression of Coulomb’s Law is:
F = kₑ (q₁q₂ / r²)
Where:
F = Electrostatic force (Newtons, N)
q₁ = First charge (Coulombs, C)
q₂ = Second charge (Coulombs, C)
r = Distance between charges (meters, m)
kₑ = Coulomb’s constant ≈ 8.98755 × 10⁹ N·m²/C²
The calculator automatically uses the correct value of Coulomb’s constant, so you only need to enter the charge values and the distance to calculate the force.
The SI unit of electric charge is the Coulomb (C).
“One Coulomb is the amount of charge transferred by a current of one ampere in one second.”
1 Coulomb = 1 Ampere × 1 Second
Electric current is measured in amperes (A), and time in seconds (s). Using these values, the total electric charge can be calculated easily.
Coulomb’s Law was formulated in 1785 by the French physicist Charles-Augustin de Coulomb. Through careful experimentation, he established the quantitative relationship between electric charges and the forces acting between them.
Coulomb’s Law can also be written in vector form to describe both magnitude and direction of the force. Each charge exerts an equal and opposite force on the other.
$$ \vec{F}_{12} = -\vec{F}_{21} $$
The vector equation for two point charges is:
$$ \vec{F}_{12} = \frac{1}{4\pi \varepsilon_0} \frac{q_1 q_2}{r_{12}^2} \hat{r}_{12} $$
For systems with multiple charges, the total force is calculated by adding all individual forces vectorially:
$$ \vec{F} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + \dots $$
Input:
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Like charges repel because the electrostatic force between them pushes them apart. Opposite charges attract due to the direction of the force acting between them.
The SI unit of electrostatic force is the Newton (N).
ESU stands for electrostatic unit (statcoulomb), while EMU stands for electromagnetic unit (abcoulomb). These are older unit systems used in electromagnetism.
A simple example is when a plastic comb rubbed through dry hair attracts small pieces of paper due to static electricity.
The symbol “Q” represents electric charge. In electric field calculations, a small positive test charge is used to measure the strength of the electric field at a point.
Coulomb’s Law plays a vital role in understanding electrostatics and its applications in real-world technologies such as photocopiers, laser printers, and electrostatic coating systems. This calculator simplifies the process of determining the electrostatic force between charges accurately and efficiently.
Scientific textbooks on electromagnetism and standard physics references.
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