Electromagnetism · 02 / 06

Electric Potential

Electric potential turns the electric interaction into an energy landscape. Voltage compares two points on that landscape; the electric field points toward the steepest decrease in potential.

The learner question

Can we describe an electric interaction without drawing a force arrow everywhere?

Yes. Potential assigns a scalar value to each point. A charged particle's potential energy depends on both that landscape and the particle's charge.

Point-charge potential
V=kQrV = k\frac{Q}{r}
U=qVU = qV

Potential depends on the source. Potential energy also depends on the test charge.

Potential landscape

Move through the landscape and watch potential, field, and energy stay connected.

reference: V → 0 far away
Vr
potential V
8.17e+3 V
field E
3.71e+3 N/C
potential energy U
8.17e-3 J
Source charge Q2.0 μC
Position r2.2 m
Test charge q1.0 μC
landscape idea
Potential is scalar

At a point, V is one number. You do not need a direction until you take the spatial slope and recover the electric field.

landscape idea
Field points downhill in potential

In one dimension, E = -dV/dx. Stronger spatial change in potential means a stronger electric field.

landscape idea
Voltage is a difference

A voltmeter compares two points. The physically useful quantity in circuits is usually ΔV, not an absolute potential value.

Positive charges roll downhill

A positive test charge lowers its electric potential energy by moving toward lower electric potential.

Negative charges invert the energy landscape

Because U = qV, a negative charge has lower potential energy where V is larger.

Equipotentials cross field lines at right angles

Moving along an equipotential changes no electric potential, so the electric field has no component along that path.

Transfer check

A positive charge moves to a point of lower electric potential. What happens to its electric potential energy?

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