Electric Potential
Introduced| English |
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| volt/vəʊlt/ |
Voltage is like "electric height"
- A ball rolls downhill from high ground to low; a positive charge "rolls" from high voltage to low.
- Voltage measures the electric potential energy per unit charge at a point.
- It is like the height of an electric landscape — energy waiting to be released.
- The difference in voltage between two points is what drives current in a circuit.
Potential is energy per charge
- Electric potential $V$ is potential energy per unit charge: $V = \dfrac{U}{q}$.
- Its unit is the volt 伏特 ($1\ \text{V} = 1\ \tfrac{\text{J}}{\text{C}}$).
- Unlike the field, potential is a scalar — just a number at each point, no direction.
- For a point charge, $V = \dfrac{kq}{r}$, falling off as $1/r$.
Field and potential together
See how the field lines relate to the potential that falls off around a charge.
Electric potential is a scalar — a single number at each point, with no direction.
Unlike the field, potential has no direction; it is a scalar in volts.
One volt equals one joule per ____.
$1\ \text{V} = 1\ \tfrac{\text{J}}{\text{C}}$ — energy per unit charge.
Equipotentials and potential difference
- Points at the same potential form equipotential surfaces (circles around a point charge).
- No work is needed to move a charge along an equipotential.
- The potential difference $\Delta V$ between two points is the "voltage" between them.
- The energy to move a charge $q$ through $\Delta V$ is $W = q\,\Delta V$.
How much energy is needed to move a $2\ \text{C}$ charge through a potential difference of $6\ \text{V}$? Answer in $\text{J}$.
$W = q\Delta V = 2 \times 6 = 12\ \text{J}$.
How much work is needed to move a charge along an equipotential surface?
Points on an equipotential are at the same potential, so no work is needed to move between them.
Select all true statements about electric potential.
Potential is a scalar in volts, and its difference drives current. Only the field has a direction.
Why it matters for circuits
- A battery maintains a fixed potential difference across its terminals.
- That voltage is the "push" that drives charges around a circuit.
- Charges flow from high potential to low, releasing energy in the components.
- So potential is the bridge from static charges to working circuits (next topic).
Which correctly distinguishes potential from field?
Potential $V = U/q$ (scalar, volts); field $E = F/q$ (vector, N/C).
Don't confuse potential $V$ (a scalar, in volts) with the field $E$ (a vector, in $\tfrac{\text{N}}{\text{C}}$). Potential is energy per charge; the field is force per charge. And only differences in potential do work — the zero point is your choice.
How much energy does it take to move a $2\ \text{C}$ charge through a potential difference of $6\ \text{V}$?
- $W = q\,\Delta V = 2 \times 6 = 12\ \text{J}$.
That is the energy the charge gains (or gives up), depending on direction.
Electric potential $V = U/q$ (in volts) is the potential energy per unit charge — a scalar, like "electric height". For a point charge $V = kq/r$. The potential difference ($\Delta V$, the voltage) drives current, and moving charge $q$ through it takes energy $W = q\,\Delta V$.