Field and Potential - Electric Fields & Electrostatics Step by Step

Field and potential describe the same electric situation in different ways: one is local direction, the other is energy per charge.

Example

Field and potential describe the same electric situation in different ways: one is local direction, the other is energy per charge. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Field is a vector claim

At this point the field has size 4 newtons per coulomb and points to the right. That is a local force-per-charge claim.

E = 4\ \text{N/C}\qquad \text{direction: right}

Potential is a scalar budget

Potential does not need an arrow. It tells energy per coulomb relative to a reference point.

V = \frac{U}{q}

A positive charge moves downhill in potential

For a positive charge, the field direction points toward lower potential. We do not compute a voltage from this field arrow; the arrow gives direction, while potential gives the energy budget.

\text{positive charge: field direction} \Rightarrow \text{lower potential}

Vector and scalar claims answer different questions

Use the field arrow to ask which way a positive test charge is pushed. Use potential to ask how much energy each coulomb gains or loses relative to the reference.

\begin{array}{c|c|c}\text{quantity}&\text{kind}&\text{answers}\\E&\text{vector}&\text{which way per charge}\\V&\text{scalar}&\text{how much energy per charge}\end{array}

electrostatics Field is a vector claim; potential is a scalar energy budget.