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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.

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Starter track

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Electricity

Next after this: Electric Potential.

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

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Why it behaves this way

Explanation

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.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough

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.

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Frozen valuesUsing frozen 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?

Make a prediction before you reveal the next step.

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

Check your reasoning against the live bench.

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?

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 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

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Open the next concept, route, or track only when you want the current model to widen into a larger branch.

Potential and voltageElectricity