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Concept module

Electric Fields

See how source-charge sign, distance, and superposition set the electric field at one probe, then watch a test charge turn that field into a force without changing the field itself.

Interactive lab

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

Electric Fields

Drag the probe anywhere in the stage or drag either source marker to change the shared separation. The field arrows, force arrow, and scan graphs stay on the same bounded model.

Graphs

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

Horizontal field scan

Shows how each source contributes to E_x and how those contributions add along the current horizontal scan line.

probe x-position (m): -3.2 to 3.2horizontal field component: -2 to 2

Source A E_xSource B E_xNet E_x

Hover or scrub to link the graph back to the stage.probe x-position (m) / horizontal field component

Controls

Adjust the physical parameters and watch the motion respond.

Source A charge

q_{A}

2 q

Positive values push the field away from Source A and negative values pull it toward Source A.

Source B charge

q_{B}

-2 q

Changing Source B lets the second contribution reinforce, cancel, or reverse the net field.

Source separation

s

2.4 m

Moves both sources symmetrically along the horizontal axis without breaking the bounded layout.

Probe x-position

x_{p}

0 m

Moves the probe left or right across both the stage and the 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}

1 m

Moves the probe to a new horizontal scan line so the graphs sample a different field slice.

Test charge

q_{test}

1 q

Changes only the force on the probe charge. It does not change the field created by the sources.

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

The net scan curve is not a separate rule. It is the point-by-point sum of the amber and sky source curves on the same y-level.

Try this

Open the horizontal scan graph and move the probe along the dashed scan line. The probe marker and the graph preview should stay synchronized.

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 strength and sign of Source A, so its local field contribution can push away or pull toward the probe.

Graph: Horizontal field scanGraph: Vertical direction and strengthOverlay: Field gridOverlay: Field vectors

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: Horizontal field scan

The net scan curve is not a separate rule. It is the point-by-point sum of the amber and sky source curves on the same y-level.

Try this

Open the horizontal scan graph and move the probe along the dashed scan line. The probe marker and the graph preview should stay synchronized.

Why it matters

It turns superposition into an observable graph relationship instead of a memorized slogan.

Control: Probe x-positionControl: Probe y-positionGraph: Horizontal field scanOverlay: Field vectorsOverlay: Graph scan line

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

Field grid

Shows a coarse sample of the field direction across the stage.

What to notice

Each tiny arrow already includes both source contributions at that location.

Why it matters

It keeps superposition visible across the plane instead of only at the current probe.

Control: Source A chargeControl: Source B chargeControl: Source separationGraph: Horizontal field scanGraph: Vertical direction and strengthEquation

q_{A}

Equation

q_{B}

Equation

s

Challenge mode

Tune the same two-charge stage into compact field targets. The checklist reads the live superposition state instead of a detached answer key.

0/2 solved

TargetCore

3 of 8 checks

Build the upward field

Starting from Dipole reference, turn the source pair into an equal positive arch so the horizontal field cancels while the net field still points upward.

Graph-linkedGuided start2 hints

Suggested start

Use the direction scan and the probe vectors together while you tune the source pair.

Pending

Open the Vertical direction and strength graph.

Horizontal field scan

Matched

Keep the Field vectors visible.

Matched

Keep the Graph scan line 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 field x between -0.08 and 0.08.

1.26

Pending

Keep field y between 1.35 and 1.48.

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

At the probe (0 m, 1 m), charges 2 q and -2 q separated by 2.4 m produce E_x = 1.26 and E_y = 0, so the net field is 1.26 in field units and points right. The test charge is 1 q, so the force is 1.26 in force units and points right. Because the test charge is positive, the force arrow stays aligned with the field.

Equation detailsDeeper interpretation, notes, and worked variable context.

Symmetric source positions

The shared separation control places Source A and Source B 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

Field from one source

Each source contributes a radial field whose direction follows the sign of the source charge and whose size falls with distance.

E_{i} = k \frac{q _{i}}{r _{i}^{3}} r_{i}

Positive q_i pushes the field away from the source.

Negative q_i pulls the field toward the source.

q_{A}

Source A charge 2 q

q_{B}

Source B charge -2 q

x_{p}

Probe x-position 0 m

y_{p}

Probe y-position 1 m

Field-strength trend

Doubling source charge doubles the field at the same point, while increasing distance quickly weakens it.

∣ E ∣ \propto \frac{∣ q ∣}{r ^{2}}

q_{A}

Source A charge 2 q

q_{B}

Source B charge -2 q

s

Source separation 2.4 m

Superposition

The net field at one probe point is the vector sum of all source contributions evaluated at that same point.

E_{net} = E_{A} + E_{B}

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 m

y_{p}

Probe y-position 1 m

Force on the test charge

A positive test charge follows the field direction, while a negative test charge reverses the force.

F_{test} = q_{test} E_{net}

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 2 compact tasks 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 1 of 60 / 6 complete

Electricity

Next after this: Electric Potential.

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

This concept is the track start.

See next concept

Short explanation

What the system is doing

An electric field tells you what a positive test charge would feel at a point before you place that test charge there. Source-charge sign sets the field direction, source strength and distance set the field size, and the net field comes from vector addition at one shared location.

This module keeps two source charges on one bounded axis and one movable probe in charge. The same source signs, separation, probe position, and test-charge sign determine the stage arrows, scan graphs, worked examples, prediction prompts, and quick test so superposition never drifts into a detached worksheet.

Key ideas

01Positive source charges send the field away from themselves, while negative source charges pull the field toward themselves.

02Field strength grows with source charge and drops quickly with distance, so nearby sources dominate the local vector.

03The test charge does not create the field in this model. It only turns the existing field into a force through F = q_test E.

Live field checks

Solve the exact state on screen.

Solve the current probe state directly from the live controls. The substitutions use the same source signs, separation, and probe point now on screen, and the force example updates instantly when you flip the test-charge sign.

Live valuesFollowing current parameters

For the current source pair and probe point, what net field vector acts 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 m

y_{p}

Probe y-position

1 m

1. Place the two sources on the shared axis

With symmetric placement,

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

and

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

2. Build the source-to-probe vectors

r_{A} = (1.2, 1)

with

∣ r_{A} ∣ = 1.56

, and

r_{B} = (- 1.2, 1)

with

∣ r_{B} ∣ = 1.56

3. Evaluate each field contribution

E_{A} = q_{A} r_{A} /∣ r_{A} ∣^{3} = (0.63, 0.52)

and

E_{B} = q_{B} r_{B} /∣ r_{B} ∣^{3} = (0.63, - 0.52)

4. Add the vectors at the same probe point

E_{net} = E_{A} + E_{B} = (1.26, 0)

, so

∣ E ∣ = 1.26

Net field

E_{net} = (1.26, 0), ∣ E ∣ = 1.26

The two source contributions are closely balanced here, so the net field comes from careful vector addition rather than one source simply dominating.

Charge-sign checkpoint

Keep both sources equal and positive, place the probe on the horizontal midpoint, then move the probe upward. What must happen to the horizontal contributions from the two sources, and why does the net field point straight up on that symmetry line?

Prediction prompt

Predict which components cancel and which components reinforce before you drag the probe.

Check your reasoning

The horizontal contributions stay equal in size and opposite in direction, so they cancel. The vertical contributions point upward together, so the net field points straight up.

Symmetry matters because both sources sit the same distance from the midpoint line. Equal distance and equal charge make equal-magnitude contributions there, so only the shared vertical direction survives the vector sum.

Common misconception

If the test charge becomes negative, the electric field at the probe reverses.

The electric field is set by the source charges and the probe location, not by the sign of the test charge you use to read it.

A negative test charge reverses the force direction because F = q_test E, but the field arrows and source-contribution graphs stay the same until you change a source or the probe position.

Quick test

Variable effect

Question 1 of 4

Answer from field logic, not from isolated formulas. Each question asks what the stage and graphs must mean about field direction, superposition, or force on a test charge.

A probe sits to the right of one isolated source charge. If the source changes from +2q to -2q at the same location, what must happen to the electric field 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 field region, and optional overlays for a field-sample grid, source-contribution arrows, the net field arrow, the force arrow on the test charge, and the horizontal scan line used by the graphs.

Dragging the probe changes the sampled field location directly on the stage, while dragging either source marker changes the shared source separation symmetrically. The focused probe handle also responds to arrow keys, and the source handles use left and right arrows to nudge separation with Home and End shortcuts for the minimum and maximum spacing. Sliders provide the same controls for source-charge sign and size, separation, probe position, and test-charge sign.

Very near a source marker, the field display uses a minimum sampling radius so the drawn arrows stay finite and readable. This keeps the visualization bounded while still preserving the correct trend that field strength grows rapidly near a charge.

Graph summary

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

The direction-and-strength graph plots the net vertical component and the total field strength along that same scan line. The force arrow on the stage depends on the current test charge, but the graphs remain field-only readouts generated by the source charges.

Keep the field story moving

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.

Potential and voltageElectricity

Electric Fields

See each variable before you move it.

Field grid

Build the upward field

Electricity

What the system is doing

Solve the exact state on screen.

For the current source pair and probe point, what net field vector acts at the probe?

A probe sits to the right of one isolated source charge. If the source changes from +2q to -2q at the same location, what must happen to the electric field at the probe?

Keep moving through the concept map.

Electric Potential

Magnetic Fields

Basic Circuits