[FEAT] Add Coulomb's Law for electrostatics (#7017)

Co-authored-by: Priyanshu1303d <priyanshu130d@gmail.com>

src/main/java/com/thealgorithms/maths/JugglerSequence.java

@@ -43,7 +43,7 @@ public final class JugglerSequence {
             seq.add(n + "");
         }
         String res = String.join(",", seq);
-        System.out.println(res);
+        System.out.print(res + "\n");
     }
 
     // Driver code

src/main/java/com/thealgorithms/physics/CoulombsLaw.java

@@ -0,0 +1,80 @@
+package com.thealgorithms.physics;
+
+/**
+ * Implements Coulomb's Law for electrostatics.
+ * Provides simple static methods to calculate electrostatic force and circular orbit velocity.
+ *
+ * @author [Priyanshu Singh](https://github.com/Priyanshu1303d)
+ * @see <a href="https://en.wikipedia.org/wiki/Coulomb%27s_law">Wikipedia</a>
+ */
+public final class CoulombsLaw {
+
+    /** Coulomb's constant in N·m²/C² */
+    public static final double COULOMBS_CONSTANT = 8.9875517923e9;
+
+    /**
+     * Private constructor to prevent instantiation of this utility class.
+     */
+    private CoulombsLaw() {
+    }
+
+    /**
+     * Calculates the electrostatic force vector exerted by one charge on another.
+     * The returned vector is the force *on* the second charge (q2).
+     *
+     * @param q1 Charge of the first particle (in Coulombs).
+     * @param x1 X-position of the first particle (m).
+     * @param y1 Y-position of the first particle (m).
+     * @param q2 Charge of the second particle (in Coulombs).
+     * @param x2 X-position of the second particle (m).
+     * @param y2 Y-position of the second particle (m).
+     * @return A double array `[fx, fy]` representing the force vector on the second charge.
+     */
+    public static double[] calculateForceVector(double q1, double x1, double y1, double q2, double x2, double y2) {
+        // Vector from 1 to 2
+        double dx = x2 - x1;
+        double dy = y2 - y1;
+        double distanceSq = dx * dx + dy * dy;
+
+        // If particles are at the same position, force is zero to avoid division by zero.
+        if (distanceSq == 0) {
+            return new double[] {0, 0};
+        }
+
+        double distance = Math.sqrt(distanceSq);
+        // Force magnitude: k * (q1 * q2) / r^2
+        // A positive result is repulsive (pushes q2 away from q1).
+        // A negative result is attractive (pulls q2 toward q1).
+        double forceMagnitude = COULOMBS_CONSTANT * q1 * q2 / distanceSq;
+
+        // Calculate the components of the force vector
+        // (dx / distance) is the unit vector pointing from 1 to 2.
+        double fx = forceMagnitude * (dx / distance);
+        double fy = forceMagnitude * (dy / distance);
+
+        return new double[] {fx, fy};
+    }
+
+    /**
+     * Calculates the speed required for a stable circular orbit of a charged particle
+     * around a central charge (e.g., an electron orbiting a nucleus).
+     *
+     * @param centralCharge The charge of the central body (in Coulombs).
+     * @param orbitingCharge The charge of the orbiting body (in Coulombs).
+     * @param orbitingMass The mass of the orbiting body (in kg).
+     * @param radius The radius of the orbit (in m).
+     * @return The orbital speed (in m/s).
+     * @throws IllegalArgumentException if mass or radius are not positive.
+     */
+    public static double calculateCircularOrbitVelocity(double centralCharge, double orbitingCharge, double orbitingMass, double radius) {
+        if (orbitingMass <= 0 || radius <= 0) {
+            throw new IllegalArgumentException("Orbiting mass and radius must be positive.");
+        }
+
+        // We only need the magnitude of the force, which is always positive.
+        double forceMagnitude = Math.abs(COULOMBS_CONSTANT * centralCharge * orbitingCharge) / (radius * radius);
+
+        // F_c = m * v^2 / r  =>  v = sqrt(F_c * r / m)
+        return Math.sqrt(forceMagnitude * radius / orbitingMass);
+    }
+}

src/test/java/com/thealgorithms/physics/CoulombsLawTest.java

@@ -0,0 +1,100 @@
+package com.thealgorithms.physics;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.DisplayName;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the CoulombsLaw utility class.
+ */
+final class CoulombsLawTest {
+
+    // A small tolerance (delta) for comparing floating-point numbers
+    private static final double DELTA = 1e-9;
+    private static final double K = CoulombsLaw.COULOMBS_CONSTANT;
+
+    @Test
+    @DisplayName("Test repulsive force between two charges on the x-axis")
+    void testSimpleRepulsiveForce() {
+        // Two positive 1C charges, 1 meter apart.
+        // Force on q2 should be F = K*1*1 / 1^2 = K, directed away from q1 (positive x)
+        double[] forceOnB = CoulombsLaw.calculateForceVector(1.0, 0, 0, 1.0, 1, 0);
+        assertArrayEquals(new double[] {K, 0.0}, forceOnB, DELTA);
+
+        // Force on q1 should be equal and opposite (negative x)
+        double[] forceOnA = CoulombsLaw.calculateForceVector(1.0, 1, 0, 1.0, 0, 0);
+        assertArrayEquals(new double[] {-K, 0.0}, forceOnA, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test attractive force between two charges on the x-axis")
+    void testSimpleAttractiveForce() {
+        // One positive 1C, one negative -1C, 1 meter apart.
+        // Force on q2 should be F = K*1*(-1) / 1^2 = -K, directed toward q1 (negative x)
+        double[] forceOnB = CoulombsLaw.calculateForceVector(1.0, 0, 0, -1.0, 1, 0);
+        assertArrayEquals(new double[] {-K, 0.0}, forceOnB, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test electrostatic force in a 2D plane (repulsive)")
+    void test2DRepulsiveForce() {
+        // q1 at (0,0) with charge +2C
+        // q2 at (3,4) with charge +1C
+        // Distance is 5 meters.
+        double magnitude = K * 2.0 * 1.0 / 25.0; // 2K/25
+        // Unit vector from 1 to 2 is (3/5, 4/5)
+        double expectedFx = magnitude * (3.0 / 5.0); // 6K / 125
+        double expectedFy = magnitude * (4.0 / 5.0); // 8K / 125
+
+        double[] forceOnB = CoulombsLaw.calculateForceVector(2.0, 0, 0, 1.0, 3, 4);
+        assertArrayEquals(new double[] {expectedFx, expectedFy}, forceOnB, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test overlapping charges should result in zero force")
+    void testOverlappingCharges() {
+        double[] force = CoulombsLaw.calculateForceVector(1.0, 1.5, -2.5, -1.0, 1.5, -2.5);
+        assertArrayEquals(new double[] {0.0, 0.0}, force, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test circular orbit velocity with simple values")
+    void testCircularOrbitVelocity() {
+        // v = sqrt( (K*1*1 / 1^2) * 1 / 1 ) = sqrt(K)
+        double velocity = CoulombsLaw.calculateCircularOrbitVelocity(1.0, 1.0, 1.0, 1.0);
+        assertEquals(Math.sqrt(K), velocity, DELTA);
+    }
+
+    @Test
+    @DisplayName("Test orbital velocity for a Hydrogen atom (Bohr model)")
+    void testHydrogenAtomVelocity() {
+        // Charge of a proton
+        double protonCharge = 1.602176634e-19;
+        // Charge of an electron
+        double electronCharge = -1.602176634e-19;
+        // Mass of an electron
+        double electronMass = 9.1093837e-31;
+        // Bohr radius (avg distance)
+        double bohrRadius = 5.29177e-11;
+
+        double expectedVelocity = 2.1876917e6;
+
+        double velocity = CoulombsLaw.calculateCircularOrbitVelocity(protonCharge, electronCharge, electronMass, bohrRadius);
+        // Use a wider delta for this real-world calculation
+        assertEquals(expectedVelocity, velocity, 1.0);
+    }
+
+    @Test
+    @DisplayName("Test invalid inputs for orbital velocity throw exception")
+    void testInvalidOrbitalVelocityInputs() {
+        // Non-positive mass
+        assertThrows(IllegalArgumentException.class, () -> CoulombsLaw.calculateCircularOrbitVelocity(1, 1, 0, 100));
+        assertThrows(IllegalArgumentException.class, () -> CoulombsLaw.calculateCircularOrbitVelocity(1, 1, -1, 100));
+        // Non-positive radius
+        assertThrows(IllegalArgumentException.class, () -> CoulombsLaw.calculateCircularOrbitVelocity(1, 1, 1, 0));
+        assertThrows(IllegalArgumentException.class, () -> CoulombsLaw.calculateCircularOrbitVelocity(1, 1, 1, -100));
+    }
+}