Physics · Electricity

Electric Fields

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Wrap-up

What you learned

Recommended next: Open concept testCheck whether the core ideas are ready without leaving this concept.
Read next: Electric PotentialPotential and voltage

Key takeaway

Source-charge sign chooses whether field points away from or toward that source.
The net electric field is a vector sum at one probe point.
A test charge changes the force reading, not the source-generated field.

Common misconception

Do not use the test-charge sign to redraw the electric field; use it only after the field is already known.

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

Continue with related ideas

Keep this idea moving

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Potential and voltageElectricity

Electric Potential

Map how source-charge sign and distance shape electric potential, read voltage as a difference across one shared horizontal scan line, and connect the downhill slope of V to the electric field.

Current-made fieldsMagnetism

See how current direction, wire spacing, distance, and superposition set the magnetic field around one or two long straight wires, with the stage arrows and scan graphs tied to the same live source pattern.

Next in Charge storageElectricity

Capacitance and Stored Electric Energy

Keep one parallel-plate capacitor on screen so geometry, stored charge, field strength, and stored electric energy stay tied to the same bounded battery-and-plates model.

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Reference and support

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Equation snapshotField first, force second · Net field by superpositionShow 3 equations

Keep the source-field rule, vector sum, and test-charge force relationship side by side.

Field first, force second
$E_{i} = k \frac{q _{i}}{r _{i}^{3}} r_{i}$
At the probe, each source creates a radial field. The sign of q_i sets whether the field points away from or toward the source, and the size shrinks with distance.
Net field by superposition
$E_{net} = E_{A} + E_{B}$
Evaluate each source's field at the same probe point, then add the vectors.
Force on the test charge
$F_{test} = q_{test} E_{net}$
Once the field is known, the test charge sets the force size and can reverse the force direction.

Why it behaves this way

Explanation

An electric field answers a concrete question: if a tiny positive test charge were placed here, which way would it start moving, and how strongly? Source-charge sign sets the field direction, source strength and distance set the size, and the net field comes from adding all source vectors at one shared point.

In this module, one live setup drives everything at once: the stage arrows, scan graphs, worked examples, prediction prompts, quick test, and challenges all use the same source signs, separation, probe position, and test-charge sign. That keeps superposition tied to what you can actually change and observe.

Key ideas

01At any point, the electric field points in the direction a positive test charge would accelerate.

02A stronger source or a nearer source contributes a larger field, so nearby charges often dominate the local vector sum.

03The net field is found by adding the source contributions at the same probe point. The test charge changes the force through F = q_test E, not the field itself.

Worked examples

Work from the live setup

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Read the values from the setup now on screen, then solve that exact case. The substitutions come from the same source signs, separation, and probe position shown on the stage, and the force example updates immediately when you change the test-charge sign.

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Example 1 of 2

Frozen valuesUsing frozen parameters

Using the source pair and probe position now on screen, what is the net field vector 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. Read the two source positions from the shared separation

With symmetric placement,

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

and

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

2. Form the vectors from each source to the probe

r_{A} = (1.2, 1)

with

∣ r_{A} ∣ = 1.56

, and

r_{B} = (- 1.2, 1)

with

∣ r_{B} ∣ = 1.56

3. Compute each source's field contribution at the probe

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 two contributions at that same point

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

, so

∣ E ∣ = 1.26

Net field

E_{net} = (1.26, 0), ∣ E ∣ = 1.26

這裡兩個來源的貢獻相當接近，因此淨電場必須靠仔細的向量疊加來判讀，而不是單靠其中一個來源主導。

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The stage keeps two source charges, one movable probe, field arrows, and the test-charge force arrow in one bounded view.

Drag the probe to sample a new point, drag either source to change the shared separation, or use the sliders for source signs, probe position, and test-charge sign. The same controls drive the stage and graphs.

Near a source, the arrows are capped for readability, but the trend remains: field strength rises quickly as distance shrinks.

Graph summary

The horizontal field-scan graph plots Source A, Source B, and net E_x along the current scan line. Where the net curve crosses zero, the horizontal contributions cancel.

The direction-and-strength graph plots net E_y and |E| on that same line. The force arrow can flip with q_test, but the graphs remain field-only readouts from the source charges.

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