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diff --git a/src/physics/test4.test.ts b/src/physics/test4.test.ts
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+import { describe, expect, it } from 'vitest';
+import { assembledEnergy, centralWork, dipoleState, energyTransfer, uniformWork } from './test4';
+
+describe('Test 4 physical answers', () => {
+  it('uses only displacement along the uniform field and preserves the charge sign', () => {
+    expect(uniformWork(2e-9, 100, 3, Math.PI / 3)).toBeCloseTo(3e-7, 14);
+    expect(uniformWork(-2e-9, 100, 3, 0)).toBeCloseTo(-6e-7, 14);
+    expect(uniformWork(2e-9, 100, 3, Math.PI / 2)).toBeCloseTo(0, 14);
+  });
+  it('computes point-charge work including the analytic infinity reference', () => {
+    expect(centralWork(3e-9, 2e-9, 2, 4)).toBeCloseTo(1.348132768845e-8, 16);
+    expect(centralWork(3e-9, -2e-9, 2, Infinity)).toBeCloseTo(-2.69626553769e-8, 16);
+    expect(() => centralWork(1, 1, 0, 2)).toThrow(RangeError);
+  });
+  it('converts the potential drop to kinetic energy without changing total energy', () => {
+    const state = energyTransfer(3e-8, 1e-8, 5e-9, 1e-6);
+    expect(state.kinetic).toBeCloseTo(2.5e-8, 16);
+    expect(state.total).toBeCloseTo(3.5e-8, 16);
+    expect(state.speed).toBeCloseTo(0.22360679775, 10);
+    expect(() => energyTransfer(0, 1, 0, 1)).toThrow(RangeError);
+  });
+  it('counts each pair once when building a charge configuration', () => {
+    const charges = [
+      { x: 0, y: 0, z: 0, coulombs: 1e-9 },
+      { x: 1, y: 0, z: 0, coulombs: 1e-9 },
+      { x: 0, y: 0, z: 0.75, coulombs: -1e-9 },
+    ];
+    expect(assembledEnergy(charges.slice(0, 1))).toBe(0);
+    expect(assembledEnergy(charges)).toBeCloseTo(-1.0185892031273e-8, 16);
+    expect(() => assembledEnergy([charges[0], charges[0]])).toThrow(RangeError);
+  });
+  it('distinguishes signed restoring torque, rotation work and zero at 90 degrees', () => {
+    const state = dipoleState(2e-9, 100, Math.PI / 2, 0);
+    expect(state.energy).toBeCloseTo(0, 14);
+    expect(state.torqueZ).toBeCloseTo(-2e-7, 14);
+    expect(state.work).toBeCloseTo(-2e-7, 14);
+    const aligned = dipoleState(2e-9, 100, 0, Math.PI / 2);
+    expect(aligned.energy).toBeCloseTo(-2e-7, 14);
+    expect(aligned.work).toBeCloseTo(2e-7, 14);
+    expect(dipoleState(2e-9, 100, Math.PI, 0).energy).toBeCloseTo(2e-7, 14);
+  });
+});