Electric Potential Energy
Energy of two interacting charges.
Formula
Variables
How it works
This formula gives the electric potential energy stored by two point charges because of their positions relative to each other. It comes from the work needed to bring the charges from very far apart to a separation r against the electric force: like charges require positive work to push together, while opposite charges release energy when brought together. The constant k is Coulomb’s constant, which sets the strength of the electric interaction in vacuum or air to a very good approximation.
When to use it
Use this when you need the interaction energy of a pair of point charges, such as in electrostatics problems involving atoms, capacitors simplified to point charges, or charge configurations. It is especially useful when comparing whether a system becomes more or less stable as charges move closer or farther apart.
Worked example, step by step
Find the electric potential energy of two charges q1 = +3.0 μC and q2 = -2.0 μC separated by r = 0.50 m. Step 1: Write the formula: U = k(q1q2)/r Step 2: Substitute values with units in coulombs: U = (8.99 × 10^9 N·m²/C²) × [(3.0 × 10^-6 C)(-2.0 × 10^-6 C)] / 0.50 m Step 3: Multiply the charges: (3.0 × 10^-6)(-2.0 × 10^-6) = -6.0 × 10^-12 C² Step 4: Divide by the distance: (-6.0 × 10^-12) / 0.50 = -1.2 × 10^-11 C²/m Step 5: Multiply by k: U = (8.99 × 10^9)(-1.2 × 10^-11) J = -0.108 J Final answer: U ≈ -0.11 J
Common mistakes to avoid
- Forgetting that charges must be converted to coulombs before substituting
- Using the wrong sign: opposite charges give negative potential energy, like charges give positive potential energy
- Confusing electric potential energy with electric potential; this formula is for energy, not voltage
Did You Know?
Storing charge takes work, and that stored electrical potential energy is what a capacitor releases in a camera flash.
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