Electric Potential Energy of Two Charges

Two positive charges push each other apart. To slide them closer together, you have to shove against that push, and the work you do doesn't vanish - it gets stored as electric potential energy, the same way lifting a rock stores gravitational energy. The formula is U = kq1q2/r, where k = 8.99 x 10⁹ N m²/C^2. As you slide two positive charges closer, r shrinks, so U climbs: you're loading energy into the pair, like compressing a spring. Let go, and that stored energy converts back into kinetic energy as the charges shoot apart.

Opposite charges flip the story. Bringing a positive and a negative charge together doesn't take outside work - they pull each other in, releasing energy as they go. That's why U comes out negative for opposite-sign pairs: negative U means the pair is bound, held together, and you'd need to add energy to pull them apart. Positive U means the opposite - the pair is repelling, and separating them happens on its own. This is the key difference from gravitational potential energy, which is always negative because gravity only attracts. Electric potential energy carries a sign that reports the relationship between the charges, not just the distance.

This sits right next to electric potential (V = kq/r), the energy per unit charge at a point in space, and electric field, the force per unit charge. Potential energy is what you get when you actually place a second charge into that field or potential and ask how much energy the pair shares.