What is Electric Potential? Think of it as the “height” of an electric hill. Just like a ball rolls downhill, a positive charge moves from high potential to low potential. The higher the hill, the more energy the charge can gain or lose.
When two point charges \$Q\$ and \$q\$ are separated by a distance \$r\$, the energy stored in the electric field is:
Potential Energy \$U\$ = \$Qq\$ / (4πϵ₀r)
This formula tells us how much energy is involved when the charges are at a certain distance. It’s like calculating how much work is needed to lift a weight to a certain height.
\$U = \dfrac{(2\times10^{-6})(-3\times10^{-6})}{4\pi(8.85\times10^{-12})(0.05)} \approx -0.27\,\text{J}\$
| Symbol | Meaning | Units |
|---|---|---|
| \$V\$ | Electric potential | Volts (V) |
| \$U\$ | Electric potential energy | Joules (J) |
| \$Q, q\$ | Point charges | Coulombs (C) |
| \$r\$ | Separation distance | Metres (m) |
Remember: When you see a question about potential energy between two charges, always write the formula first, then plug in the numbers. Check the sign of the charges – positive × positive gives positive energy (repulsion), positive × negative gives negative energy (attraction). Also, keep an eye on units: 1 C = 1 A·s, 1 V = 1 J/C.
Two charges, \$Q = 5\,\mu\text{C}\$ and \$q = 4\,\mu\text{C}\$, are 0.10 m apart. What is the electric potential energy? Show your steps.
Solution: \$U = \dfrac{(5\times10^{-6})(4\times10^{-6})}{4\pi(8.85\times10^{-12})(0.10)} \approx 0.57\,\text{J}\$ (positive, so the charges repel).
• Electric potential tells you the “hill height” for a charge.
• Multiply that hill by the charge to get the energy stored.
• Use the formula \$U = \dfrac{Qq}{4\pi\epsilon_0 r}\$ and remember the sign of the charges.
• Practice with different charge signs and distances to build confidence for the exam. 🚀