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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.

Interactive lab

Keep the stage, graph, and immediate control feedback in one working view.

Electric Potential

Drag the probe anywhere in the stage or drag either source marker to change the shared separation. Warm regions are positive potential, cool regions are negative, and the field arrow shows the downhill direction on that same map.

Graphs

Switch graph views without breaking the live stage and time link.

Potential along scan line

Source A, Source B, and the net potential are sampled along the same horizontal scan line. Vertical separation between two x-positions is a potential difference.

probe x on current scan line (m): -3.2 to 3.2potential V (arb. units): -4 to 4

Source A VSource B VNet V

Hover or scrub to link the graph back to the stage.probe x on current scan line (m) / potential V (arb. units)

Controls

Adjust the physical parameters and watch the motion respond.

Source A charge

q_{A}

2 q

Positive values raise nearby potential and negative values lower it.

Source B charge

q_{B}

-2 q

Changing Source B lets the second potential contribution reinforce, weaken, or reverse the net value.

Source separation

s

2.4 m

Moves both sources symmetrically without breaking the bounded layout.

Probe x-position

x_{p}

-0.8 m

Moves the probe left or right across the stage and linked scan graphs.

More tools

Secondary controls, alternate presets, and less-used toggles stay nearby without crowding the main bench.

Hide

Probe y-position

y_{p}

0.8 m

Moves the probe to a different horizontal scan line.

Test charge

q_{test}

1 q

Changes only the potential energy U = qV, not the potential itself.

More presets

Presets

Predict -> manipulate -> observe

Keep the active prompt next to the controls so each change has an immediate visible consequence.

Graph readingPrompt 1 of 2

Potential difference is a vertical gap on the same V(x) curve, not a separate object. Moving the probe along the scan line changes the readout and the graph together.

Try this

Hover two different x-locations on the potential graph and compare the stage preview and the readout card.

Equation map

See each variable before you move it.

Select a symbol to highlight the matching control and the graph or overlay it most directly changes.

q_{A}

Source A charge

2 q

Changes the sign and size of Source A, which raises or lowers the nearby potential map and reshapes the scan curves.

Graph: Potential along scan lineGraph: Slope-to-field linkOverlay: Potential mapOverlay: Equipotential contours

Equations in play

Choose an equation to sync the active symbol, control highlight, and related graph mapping.

More tools

Detailed noticing prompts, guided overlays, and challenge tasks stay available without taking over the main bench.

Hide

What to notice

Use the current prompt as a compact investigation cue. Each one points at a pattern the stage and graphs already show in the live state.

Graph readingPrompt 1 of 2

Graph: Potential along scan line

Potential difference is a vertical gap on the same V(x) curve, not a separate object. Moving the probe along the scan line changes the readout and the graph together.

Try this

Hover two different x-locations on the potential graph and compare the stage preview and the readout card.

Why it matters

Voltage becomes more intuitive when it is read as a change between two positions on one shared graph.

Control: Probe x-positionControl: Probe y-positionGraph: Potential along scan lineOverlay: Scan lineOverlay: Potential map

Guided overlays

Focus one overlay at a time to see what it represents and what to notice in the live motion.

4 visible

Overlay focus

Potential map

Shows signed potential across the stage with warm colors for positive V and cool colors for negative V.

What to notice

The map already includes both source contributions at each point.

Why it matters

Potential difference becomes visible as a height change on one shared landscape rather than a detached number.

Control: Source A chargeControl: Source B chargeControl: Source separationGraph: Potential along scan lineEquation

q_{A}

Equation

q_{B}

Equation

s

Challenge mode

Use the shared two-charge map for compact voltage targets. The checklist reads the live potential and field link, not a separate answer sheet.

0/1 solved

TargetCore

3 of 10 checks

Positive midpoint plateau

Starting from Dipole reference, tune the setup until the midpoint has almost zero field but still sits on a clearly positive potential hill.

Graph-linkedGuided start2 hints

Suggested start

Use the field-link graph and the field arrow together while you tune the midpoint.

Pending

Open the Slope-to-field link graph.

Potential along scan line

Matched

Keep the Potential map visible.

Matched

Keep the Field arrow visible.

Matched

Keep source charge a between 1.9 q and 2.1 q.

2 q

Pending

Keep source charge b between 1.9 q and 2.1 q.

-2 q

Pending

Keep source separation between 1.95 m and 2.05 m.

2.4 m

Pending

Keep probe x between -0.05 m and 0.05 m.

-0.8 m

Pending

Keep probe y between -0.05 m and 0.05 m.

0.8 m

Pending

Keep potential between 3.8 and 4.2.

1.31

Pending

Keep field magnitude between 0 and 0.08.

2.57

The checklist updates from the live simulation state, active graph, overlays, inspect time, and compare setup.

At the probe (-0.8 m, 0.8 m), charges 2 q and -2 q separated by 2.4 m give V_A = 2.24 and V_B = -0.93, so the net potential is 1.31. The probe sits in a positive-potential region. The local field magnitude is 2.57 and The field points up-right, which is the downhill direction on the potential map. For q_test = 1 q, the potential energy is 1.31. The test charge has positive potential energy here.

Equation detailsDeeper interpretation, notes, and worked variable context.

Symmetric source positions

The shared separation control places the two source charges equally far from the origin on the horizontal axis.

x_{A} = - \frac{s}{2}, x_{B} = + \frac{s}{2}

s

Source separation 2.4 m

Potential from one source

A positive source contributes positive potential, a negative source contributes negative potential, and the magnitude falls with distance.

V_{i} = k \frac{q _{i}}{r _{i}}

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

Scalar superposition

Net potential is the signed sum of the source contributions at one point.

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

q_{A}

Source A charge 2 q

q_{B}

Source B charge -2 q

Field from potential

The electric field points in the direction of the steepest drop in potential.

E = - \nabla V

Horizontal scan-line link

Along the current horizontal slice, the x-component of the field is the negative slope of the potential graph.

E_{x} = - \frac{d V}{d x}

s

Source separation 2.4 m

x_{p}

Probe x-position -0.8 m

y_{p}

Probe y-position 0.8 m

Potential energy

Changing the sign of the test charge changes the sign of U without changing the potential set by the sources.

U = q_{test} V

q_{test}

Test charge 1 q

Progress

Not startedMastery: NewLocal-first

Start exploring and Open Model Lab will keep this concept's progress on this browser first. Challenge mode has 1 compact task ready. No finished quick test, solved challenge, or completion mark is saved yet.

Let the live model runChange one real controlOpen What to notice

Try this setup

Copy the live bench state and reopen this concept with the same controls, graph, overlays, and compare context.

Stable links

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

Short explanation

What the system is doing

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.

Live potential checks

Solve the exact state on screen.

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.

Live valuesFollowing current 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?

Prediction prompt

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

Check your reasoning

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?

Choose one answer to reveal feedback, then test the idea in the live system if a guided example is available.

Accessible description

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.

Connect this voltage view

Keep moving through the concept map.

These suggestions come from the concept registry, so the reason label reflects either curated guidance or the fallback progression logic.

Reuse voltage in circuitsElectricity

Electric Potential

See each variable before you move it.

Potential map

Positive midpoint plateau

Electricity

What the system is doing

Solve the exact state on screen.

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

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

Keep moving through the concept map.

Basic Circuits

Power and Energy in Circuits

Series and Parallel Circuits