Physics · Electricity

Electric Potential

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Wrap-up

What you learned

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Read next: RC Charging and DischargingTurn storage into time response

Key takeaway

A zero electric field means the local slope of potential is zero there. It does not automatically mean the potential itself is zero.
Along a horizontal scan line, the electric field depends on how quickly the potential changes with position: a steeper downhill slope means a stronger field.

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 potential has zero local slope there, not that the potential value must be zero.

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Equation snapshotSymmetric source positions · Potential from one sourceShow 2 equations

Symmetric source positions
$x_{A} = - \frac{s}{2}, x_{B} = + \frac{s}{2}$
The shared separation control places the two source charges equally far from the origin on the horizontal axis.
Potential from one source
$V_{i} = k \frac{q _{i}}{r _{i}}$
Each source contributes a signed scalar potential. Positive charges raise V, negative charges lower V, and the magnitude decreases with distance.

Why it behaves this way

Explanation

Electric potential tells you how much electric potential energy a positive test charge would have per unit charge at a location. Positive source charges raise the potential, negative source charges lower it, and nearby sources change it more strongly than distant ones.

Because potential is a scalar, you add signed values, not directions. That is why the midpoint between two equal positive charges can have zero electric field but still positive potential. Along the current scan line, the electric field is linked to the potential graph by slope: where V falls as x increases, E_x points in the positive x-direction.

Key ideas

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

02A zero electric field means the local slope of potential is zero there. It does not automatically mean the potential itself is zero.

03Along a horizontal scan line, the electric field depends on how quickly the potential changes with position: a steeper downhill slope means a stronger field.

Worked examples

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Frozen walkthrough

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Frozen walkthrough

Read the values from the setup now on screen, then solve that exact case. The same source signs, distances, and test-charge sign drive the potential map, the linked graphs, and the numerical results below.

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Example 1 of 2

Frozen valuesUsing frozen parameters

Using the current source pair and probe position, what net electric potential is present 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. Read the two source positions from the separation

Symmetric placement gives

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

and

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

2. Measure the probe's distance from each source

The probe is

r_{A} = 0.89

from Source A and

r_{B} = 2.15

from Source B.

3. Compute each signed potential contribution

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.

Quick test

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Accessibility

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The simulation shows two source charges on a horizontal axis, a movable probe 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 near a source for readability, but the readout and graphs still preserve the correct trend that the 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 that same x-location on the stage.

The field-link 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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Step 2 of 6

Electricity

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