Electric potential and capacitor energy connect electric fields to energy, voltage, and circuit behavior. This cheat sheet helps students quickly compare potential, potential energy, capacitance, and stored energy. These ideas are needed for electrostatics, circuits, and understanding how devices store and release electrical energy.
Clear formulas also help prevent mixing up charge, voltage, energy, and field strength.
Electric potential is energy per unit charge, so and a potential difference is . For a point charge, the potential is , and for a uniform electric field, when moving with the field. A capacitor stores charge according to and stores energy given by , , or .
For a parallel-plate capacitor, , so larger plate area increases capacitance and larger separation decreases capacitance.
Key Facts
- Electric potential is electric potential energy per unit charge, written as .
- Electric potential difference is the change in potential energy per unit charge, written as .
- The electric potential from a point charge is , where .
- Electric potential energy for two point charges is .
- In a uniform electric field, the potential difference over distance along the field is .
- Capacitance is the charge stored per volt, written as .
- The energy stored in a capacitor can be calculated using , , or .
- For a parallel-plate capacitor, , where is plate area, is separation, and is the permittivity of the material between plates.
Vocabulary
- Electric Potential
- Electric potential is the electric potential energy per unit charge at a location, measured in volts.
- Potential Difference
- Potential difference is the change in electric potential between two points, written as .
- Electric Potential Energy
- Electric potential energy is the energy a charge has because of its position in an electric field.
- Capacitance
- Capacitance is a measure of how much charge a capacitor stores for each volt of potential difference.
- Capacitor
- A capacitor is a device that stores separated charge and electric energy between conductors.
- Permittivity
- Permittivity is a material property that affects how strongly an electric field forms inside a material.
Common Mistakes to Avoid
- Confusing electric potential with electric potential energy is wrong because , so potential is energy per charge while energy depends on the amount of charge.
- Dropping the sign of charge is wrong because formulas such as depend on whether charges are positive or negative.
- Using distance from the wrong point is wrong because uses the distance from the source charge to the location being analyzed.
- Forgetting the square in capacitor energy is wrong because means doubling voltage makes the stored energy four times larger.
- Assuming a larger plate separation increases capacitance is wrong because shows capacitance decreases as increases.
Practice Questions
- 1 A charge has electric potential energy at a point where its charge is . What is the electric potential at that point?
- 2 A capacitor has capacitance and is connected across a potential difference of . How much charge is stored?
- 3 A capacitor has and . Find the stored energy using .
- 4 A battery remains connected to a parallel-plate capacitor while the plate separation is increased. Explain what happens to the capacitance, charge stored, and stored energy.
Understanding Electric Potential & Capacitor Energy
Voltage is easiest to understand as an energy landscape. A positive test charge naturally moves from higher electric potential toward lower electric potential, much like an object moving downhill. A negative charge behaves in the opposite direction because its charge has the opposite sign.
This is why the sign of charge matters in every potential energy problem. The zero level of potential is a chosen reference point. For isolated charges, physicists often choose zero very far away.
In circuits, ground is commonly chosen as zero. A negative voltage does not mean something is wrong. It only means the location is below the selected reference level.
Electric fields point in the direction that a positive charge would be pushed. Along that direction, electric potential decreases. Field lines tell you the direction of change, while equipotential lines or surfaces mark places with the same potential.
Moving along one equipotential surface requires no work from the electric force because there is no change in electric potential energy. This idea helps explain why metal surfaces in electrostatic equilibrium are equipotential.
If different points on a conductor had different potentials, charges would keep moving inside it. They stop only after the potential becomes uniform throughout the conductor.
A capacitor does not create charge from nothing. When connected to a battery, electrons are moved from one plate to the other. One plate gains excess electrons and becomes negative.
The other loses electrons and becomes positive. The battery does work to separate these charges. That work becomes energy stored in the electric field in the space between the plates.
As more charge builds up, adding another small amount becomes harder because the existing charges repel it. This gradual buildup explains the one half factor in the capacitor energy expressions. The average voltage during charging is half of the final voltage.
The material between capacitor plates matters because it changes how the electric field behaves. An insulating material called a dielectric becomes slightly polarized in the field. Its positive and negative charges shift by tiny distances in opposite directions.
This reduces the effective field produced by the stored plate charges, allowing more charge to be placed on the plates at the same voltage. Real capacitors have limits.
If the voltage is too large, the electric field can tear electrons through the insulating material. This is dielectric breakdown, and it can permanently damage the component.
Capacitors appear in phone chargers, camera flashes, touch screens, computers, speakers, and power supplies. Some store energy briefly for a flash or pulse. Others smooth changing voltages by charging when voltage rises and discharging when it falls.
In calculations, keep track of what is held fixed. A capacitor connected to a battery has fixed voltage because the battery can supply or remove charge.
An isolated capacitor has fixed charge because there is no path for charge to leave. This distinction changes how capacitance, energy, plate spacing, and dielectric insertion affect the system.