Writing Python script to simulate two electrons - electrons moving in parallel directions instead of collinearly

Question

I am trying to write a Python program to simulate two electrons interacting with one another, with only the Couloumb force acting upon them. So, they should be moving in paths that are collinear with one another, but for some reason, my simulated electrons are moving in paths that are parallel to one another.

# -*- coding: utf-8 -*-
"""
Created on Wed Sep 20 10:01:24 2023

@author: sanat 
"""

import pygame
import sys
import math

# Constants
WIDTH, HEIGHT = 2000, 1000
BACKGROUND_COLOR = (255, 255, 255)
ELECTRON_RADIUS = 5
TIME_STEP = 0.01  # Time step for simulation

# Electron properties
electron1 = {
    "pos": [400, 500],
    "velocity": [0, 0],
    "charge": - 1.0,
    "mass": 1.0
}

electron2 = {
    "pos": [900, 600],
    "velocity": [0, 0],
    "charge": -1.0,
    "mass": 1.0
}

# Initialize Pygame
pygame.init()
screen = pygame.display.set_mode((WIDTH, HEIGHT))
pygame.display.set_caption("Electron Motion Simulation")

def calculate_force(e1, e2):
    k = 8.988e9  # Coulomb's constant
    r = math.sqrt((e1["pos"][0] - e2["pos"][0]) ** 2 + (e1["pos"][1] - e2["pos"][1]) ** 2)
    force = (k * e1["charge"] * e2["charge"]) / (r ** 2)
    return force

def update_velocity(electron, force):
    acceleration = force / electron["mass"]
    electron["velocity"][0] += acceleration * TIME_STEP
    electron["velocity"][1] += acceleration * TIME_STEP

def update_position(electron):
    electron["pos"][0] += electron["velocity"][0] * TIME_STEP
    electron["pos"][1] += electron["velocity"][1] * TIME_STEP

def draw_electrons():
    for electron in [electron1, electron2]:
        pygame.draw.circle(screen, (0, 0, 0), (int(electron["pos"][0]), int(electron["pos"][1])), ELECTRON_RADIUS)

running = True
while running:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            running = False

    # Calculate force between electrons
    force = calculate_force(electron1, electron2)

    # Update velocities and positions
    update_velocity(electron1, force)
    update_velocity(electron2, -force)  # Opposite force on electron2
    update_position(electron1)
    update_position(electron2)

    # Clear the screen
    screen.fill(BACKGROUND_COLOR)

    # Draw electrons
    draw_electrons()

    pygame.display.flip()
    pygame.time.delay(1000)

pygame.quit()
sys.exit()

So, that is the code that I have, and I am not quite sure where I have gone wrong.

Answer 1

Thanks to Karl, I was able to fix the code. I was missing a way to find the direction of the force vectors, and was able to resolve like so:

def calculate_force_vector(e1, e2):
    k = 8.988e9  # Coulomb's constant
    r_vector = np.array(e1["pos"]) - np.array(e2["pos"])
    r_magnitude = np.linalg.norm(r_vector)
    force_magnitude = (k * e1["charge"] * e2["charge"]) / (r_magnitude ** 2)
    force_direction = r_vector / r_magnitude  # Normalize the direction vector
    force_vector = force_magnitude * force_direction
    return force_vector