A simple simulation of two charged particles where one particle remains stationary, and the other orbits around it under the influence of Coulomb's Law. The simulation uses Julia's plotting capabilities to animate the motion of the orbiting particle and visualize the circular path.
This project simulates two charged particles interacting via Coulomb's Law. One particle is fixed at the origin while the other orbits around it in a stable circular orbit. The orbit is driven by the balance between the electrostatic force (Coulomb force) and the centripetal force required to keep the particle on its path.
- How to simulate particle motion using Coulomb's Law.
- How to use Euler's method for simple numerical integration.
- How to visualize particle motion and generate animations using Plots.jl in Julia.
- Simulates the interaction of two charged particles under Coulomb’s Law.
- Produces a GIF animation showing the orbit of one particle around the other.
- Uses dynamic plot updates to visualize the circular motion.
- Simple, adjustable parameters for charge, mass, and distance.
- Install Julia from the official Julia website.
- Clone the repository:
git clone https://github.com/hodini007/n-body-simulation cd charged-particle-orbit-simulation
Install the required Julia packages: julia Copy code using Pkg Pkg.add("Plots") Pkg.add("StaticArrays") Pkg.add("LinearAlgebra") Usage 💻 To run the simulation and generate the orbit GIF:
Open the Julia REPL or your preferred Julia IDE.
Run the main script:
julia Copy code include("circular_orbit_simulation.jl") The simulation will run, and an animated GIF (circular_orbit_fixed.gif) will be generated in the working directory.
How It Works 🔬 This simulation models the interaction of two charged particles using Coulomb’s Law:
Coulomb's Law describes the force between two charged particles:
𝑘 ⋅ ∣ 𝑞 1 ⋅ 𝑞 2 ∣ 𝑟 2 F=k⋅ r 2
∣q 1 ⋅q 2 ∣
Where:
𝑘 k is Coulomb's constant. 𝑞 1 q 1 and 𝑞 2 q 2 are the charges of the two particles. 𝑟 r is the distance between them. The orbiting particle is given an initial velocity that balances this force with the centripetal force, ensuring circular motion.
The simulation uses Euler's method for numerical integration, updating the position and velocity of the orbiting particle at each time step.
You can customize the simulation by adjusting parameters in the code:
Charge of particles (q1, q2): Modify the charge of the fixed and orbiting particles to see how different charges affect the motion. Mass of particles (m1, m2): Change the masses of the particles to influence the acceleration. Distance between particles (r): Adjust the initial distance between the two particles. Time step (dt): Change the integration time step to make the simulation more accurate or faster. Number of simulation steps (num_steps): Modify the total number of frames in the animation.
Contributions are welcome! Feel free to submit a pull request or open an issue if you have any suggestions or find a bug.
Fork the repository. Create your feature branch:
git checkout -b feature/AmazingFeature
Commit your changes:
git commit -m 'Add some AmazingFeature'
Push to the branch:
git push origin feature/AmazingFeature
Open a pull request.
This project is licensed under the MIT License - see the LICENSE file for details.
Enjoy simulating! 😎 If you find this project helpful, consider giving it a ⭐ on GitHub.