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Concept module

Electric Potential

Map how source-charge sign and distance shape electric potential, compare potential differences across one honest scan line, and connect the downhill slope of V to the electric field.

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Starter track

Step 2 of 60 / 6 complete

Electricity

Earlier steps still set up Electric Potential.

1. Electric Fields2. Electric Potential3. Basic Circuits4. Power and Energy in Circuits+2 more steps

Previous step: Electric Fields.

Start from track beginning

Why it behaves this way

Explanation

Electric potential describes the electric potential energy per unit positive test charge at a location. Positive source charges raise the potential, negative source charges lower it, and distance controls how strongly each source contributes.

This module keeps the same bounded two-charge geometry as Electric Fields so the map, equipotential cues, probe readout, worked examples, prediction prompts, and quick test all refer to one honest model. Along the current scan line, the electric field is the downhill slope of the potential graph rather than a separate disconnected rule.

Key ideas

01Electric potential is a scalar, so source contributions add by signed value rather than by vector direction.

02Equal positive charges can make the electric field zero at the midpoint while the potential there stays positive, because the field cancels as a vector but the potential adds as a scalar.

03The electric field points toward lower potential for a positive test charge. Along a horizontal scan line, a positive E_x means V decreases as x increases.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Solve the current probe state directly from the live controls. The same source signs, distances, and test-charge sign drive the potential map, the linked graphs, and the result below.

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Frozen valuesUsing frozen parameters

For the current source pair and probe point, what scalar electric potential exists at the probe?

q_{A}

Source A charge

2 q

q_{B}

Source B charge

-2 q

s

Source separation

2.4 m

x_{p}

Probe x-position

-0.8 m

y_{p}

Probe y-position

0.8 m

1. Place the two sources on the shared axis

Symmetric placement gives

x_{A} = - s /2 = - 1.2 m

and

x_{B} = + s /2 = 1.2 m

2. Measure the probe distances

The probe is

r_{A} = 0.89

from Source A and

r_{B} = 2.15

from Source B.

3. Evaluate the signed source contributions

V_{A} = q_{A} / r_{A} = 2.24

and

V_{B} = q_{B} / r_{B} = - 0.93

4. Add the scalar contributions

V_{net} = V_{A} + V_{B} = 1.31

Net potential

V_{net} = 1.31

The net potential is positive here because the positive contributions outweigh any negative contribution at this probe point.

Potential-difference checkpoint

Two equal positive charges sit symmetrically on the x-axis, and the probe is exactly halfway between them on that same axis. Why can the potential there stay positive while the net electric field is zero?

Make a prediction before you reveal the next step.

Predict whether scalar addition or vector cancellation decides each quantity before you open the midpoint preset.

Check your reasoning against the live bench.

The potential stays positive because both source contributions are positive scalars, but the electric field is zero because the two equal field vectors point in opposite directions and cancel.

Potential adds by signed value, while electric field adds by vector direction. The midpoint between equal positive charges is the cleanest place to see those rules diverge without changing any geometry.

Common misconception

If the electric field is zero at one point, the electric potential there must also be zero.

Field and potential are related, but they are not the same quantity. A zero field means the local slope of potential is zero, not that the potential itself vanishes.

At the midpoint between two equal positive charges, the field cancels because the pushes are equal and opposite, but the potential stays positive because both scalar contributions are positive.

Quick test

Variable effect

Question 1 of 5

Answer from the live potential logic, not from detached formulas. Each question asks what the map, contours, or linked graphs must mean.

A probe moves farther away from one isolated positive source charge. What must happen to the electric potential at the probe?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows two source charges on a horizontal axis, a movable probe charge inside a bounded potential region, and optional overlays for a signed potential map, equipotential contours, a field arrow at the probe, and the horizontal scan line used by the graphs.

Dragging the probe changes the sampled location directly on the stage, while dragging either source marker changes the shared source separation symmetrically. Sliders provide the same controls for source-charge sign and size, separation, probe position, and test-charge sign.

Color saturation in the potential map is clipped for readability near a source, but the numeric readout and graphs still preserve the correct trend that potential magnitude grows rapidly as the probe approaches a charge.

Graph summary

The potential-scan graph plots Source A's contribution, Source B's contribution, and the net potential along the current horizontal scan line. Hovering the graph previews the same x-location on the stage.

The slope-to-field graph plots the net horizontal field and the matching negative slope of the potential graph along that same scan line. The test-charge sign changes the potential-energy readout, but the graphs remain source-only views of V and E.

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Reuse voltage in circuitsElectricity