Coulomb’s Law: 3-Particle Net Force Calculator
An advanced tool to calculate the net electrostatic force on a point charge resulting from the influence of two other point charges, based on the principle of superposition.
Particle 1 (Calculate Force ON this particle)
Particle 2 (Source of Force)
Particle 3 (Source of Force)
Calculation Results
Net Force Magnitude on Particle 1:
Force Vector Visualization
Diagram dynamically visualizes particle positions and force vectors. The net force on q₁ is shown in green.
What is the Electric Force Calculation for Three Particles?
To calculate electric force using Coulomb’s law for 3 particles, we rely on the principle of superposition. This principle states that the total electrostatic force on a given charge is the vector sum of the individual forces exerted on it by all other charges. The presence of other charges does not alter the force between any two charges. So, to find the net force on Particle 1, we first calculate the force from Particle 2 on Particle 1 (F₂₁) and then the force from Particle 3 on Particle 1 (F₃₁). Finally, we add these two force vectors together to get the total net force.
The Formula for Calculating Net Electric Force
The foundational formula is Coulomb’s Law, which gives the magnitude of the force between two point charges.
F = k * |q₁ * q₂| / r²
To find the net force on charge q₁ from charges q₂ and q₃, we perform a vector sum:
Fnet,1 = F₂₁ + F₃₁
This is done by breaking down each force into its x and y components and then summing the components:
- Fnet,x = F₂₁ₓ + F₃₁ₓ
- Fnet,y = F₂₁ᵧ + F₃₁ᵧ
The final magnitude of the net force is found using the Pythagorean theorem, and its direction is found using the arctangent.
Variables Table
| Variable | Meaning | Unit (SI) | Typical Range |
|---|---|---|---|
| F | Electrostatic Force | Newtons (N) | Dependent on inputs |
| k | Coulomb’s Constant | N·m²/C² | ~8.987 x 10⁹ |
| q | Electric Charge | Coulombs (C) | 10⁻⁹ to 10⁻³ C (nC to mC) |
| r | Distance between charges | meters (m) | 10⁻³ to 10³ m |
| Fnet | Net Force Vector | Newtons (N) | Dependent on inputs |
Practical Examples
Example 1: Collinear Charges
Imagine three charges in a line. q₁ (+1µC) is at the origin (0,0). q₂ (-2µC) is at (2m, 0), and q₃ (+3µC) is at (-3m, 0).
- Inputs: q₁=+1µC, q₂=-2µC, q₃=+3µC. r₂₁=2m, r₃₁=3m.
- Force F₂₁: Since q₁ and q₂ have opposite signs, the force is attractive, pulling q₁ to the right (positive x-direction).
- Force F₃₁: Since q₁ and q₃ have the same sign, the force is repulsive, pushing q₁ to the right (positive x-direction).
- Result: Both forces point in the same direction, so their magnitudes add up directly for a strong net force to the right.
Example 2: Charges in a Right Triangle
Consider q₁ (+1µC) at the origin (0,0). q₂ (+2µC) is at (3m, 0) and q₃ (+2µC) is at (0, 4m).
- Inputs: q₁=+1µC, q₂=+2µC, q₃=+2µC.
- Force F₂₁: This is a repulsive force pushing q₁ along the negative x-axis.
- Force F₃₁: This is a repulsive force pushing q₁ along the negative y-axis.
- Result: The two forces are perpendicular. The net force will point down and to the left, and its magnitude is found using the Pythagorean theorem on the magnitudes of F₂₁ and F₃₁. For more on vector addition, you might find a resource on the vector addition of electric forces helpful.
How to Use This Coulomb’s Law Calculator
- Define the Particles: Enter the charge magnitude and X/Y coordinates for each of the three particles.
- Select Units: For each charge and position, select the appropriate unit from the dropdown menu (e.g., µC for charge, cm for distance). The calculator automatically handles conversions.
- Analyze the Results: The calculator provides the net force magnitude and direction on Particle 1. It also shows the intermediate forces from Particle 2 and Particle 3.
- Interpret the Visualization: The SVG chart shows the positions of the particles and the force vectors acting on Particle 1. Red arrows show forces from individual source charges, and the green arrow shows the resulting net force.
Key Factors That Affect Electric Force
- Charge Magnitude: The force is directly proportional to the product of the charges. Doubling any charge doubles the force.
- Distance: Force is inversely proportional to the square of the distance. Doubling the distance reduces the force to one-quarter of its original value.
- Sign of Charges: Like charges (both positive or both negative) result in a repulsive force, while opposite charges result in an attractive force.
- Vector Superposition: The geometry of the charges is critical. The final net force depends on the vector sum, where angles between forces can lead to constructive or destructive interference.
- Medium: The value of Coulomb’s constant (k) is for a vacuum. If the charges are in a different medium (like oil or water), the force is reduced. This calculator assumes a vacuum. Learn more about the superposition principle.
- Point Charges: Coulomb’s law is most accurate for point charges or spherically symmetric charges where the distance between them is large compared to their size.
Frequently Asked Questions (FAQ)
It states that the total force on a charge is the vector sum of the individual forces from every other charge, calculated one at a time as if the others weren’t there.
Force has both a magnitude (strength) and a direction. To combine forces correctly, we must use vector addition, which accounts for both of these properties.
A particle with zero charge will not exert or experience an electrostatic force. The calculation involving that charge will result in zero force.
It converts all user inputs (like µC, nC, cm) into the base SI units (Coulombs, meters) before performing the calculation to ensure the formula works correctly.
In this calculator, the force magnitudes are always positive. The direction is indicated by the force vector components (Fx, Fy) and the angle. A negative Fx means the force points left; a negative Fy means it points down.
This specific calculator is designed for three particles. However, the principle can be extended: for four particles, you would calculate and sum three force vectors. You can learn more about general physics principles with a free physics calculator.
If two particles are at the same coordinates, the distance ‘r’ between them is zero. Since ‘r’ is in the denominator, this would lead to a division by zero, representing an infinite force. The calculator will show an error or “Infinity” in this case.
No, this is a 2D calculator using X and Y coordinates. A 3D calculation would also require Z coordinates and involve vector math in three dimensions.