Electric potential describes how much electric potential energy a unit positive charge would have at a point in space. Voltage is the difference in electric potential between two points, so it tells how much energy is transferred per coulomb of charge. These ideas matter because they connect invisible electric fields to measurable quantities in circuits, batteries, capacitors, and particle motion.
A voltage map helps predict where charges will move and how much energy they can gain or lose.
Key Facts
- Electric potential is electric potential energy per charge: V = U/q.
- Voltage is potential difference: ΔV = VB - VA = ΔU/q.
- For a point charge, electric potential is V = kQ/r, where k = 8.99 × 10^9 N m^2/C^2.
- Electric field points in the direction of decreasing electric potential for a positive test charge.
- In a uniform electric field, ΔV = -Ed when moving distance d along the field direction.
- Equipotential lines connect points with the same electric potential, so moving a charge along one requires no work.
Vocabulary
- Electric potential
- Electric potential is the electric potential energy per unit charge at a point in an electric field.
- Voltage
- Voltage is the difference in electric potential between two points, measured in volts.
- Equipotential line
- An equipotential line is a line connecting points that all have the same electric potential.
- Electric field
- An electric field is a region where a charge experiences an electric force.
- Volt
- A volt is one joule of energy per coulomb of charge, so 1 V = 1 J/C.
Common Mistakes to Avoid
- Confusing electric potential with electric potential energy is wrong because potential is energy per unit charge, while potential energy depends on the amount of charge present.
- Thinking voltage only exists in circuits is wrong because voltage can be defined between any two points in an electric field.
- Drawing electric field lines parallel to equipotential lines is wrong because electric field lines cross equipotential lines at right angles.
- Ignoring the sign of charge is wrong because positive and negative charges move in opposite directions for the same electric field and potential difference.
Practice Questions
- 1 A charge has 0.060 J of electric potential energy at a point where the electric potential is 12 V. What is the charge?
- 2 What is the electric potential 0.30 m from a +2.0 μC point charge? Use k = 8.99 × 10^9 N m^2/C^2.
- 3 A positive charge is released from rest near a positive point charge. Explain whether it moves toward higher potential or lower potential, and connect your answer to the direction of the electric field.