SCIENCE · INVESTIGATE AND EXPLAIN

Separate electric field from force on a charge

Compare positive, negative and zero charges at one source-field location.

Learning outcome: Use F = qE, identify field direction by a positive test charge and explain nonzero field at zero probe charge.

Starting recap

The displayed field comes only from the prescribed source Q. The probe’s own field is excluded from force on itself.

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Try

Can an electric field exist where the selected charge experiences zero electric force?

Open the experiment

Predict

At 0.20 m, predict whether changing q from +2 to −2 to 0 nC changes the source field, the force, both or neither.

Your prediction and reason

Experiment

Capture those three charges at the same separation. Compare the field plot and force pair. Then double separation and compare the field magnitude.

Separate electric force, field and potential

Worked teaching model · synthetic values · Two prescribed stationary point charges in vacuum, Q = +2 nC at x = 0 and q = −4 to +4 nC to its right. Rounded Coulomb constant k = 8.99 × 10⁹ N m²/C². The field and potential shown at q are due to Q alone and exclude self-fields. Q and q remain fixed as sources for each selected scenario; controls select comparisons, not time evolution or a charge-transfer process. Mutual electric forces are equal and opposite but act on different charges. External supports that hold positions are not drawn; their forces would balance the electric forces. Potential and pair interaction energy are zero at infinite separation. Work compares the same q moved from r = 0.20 m to the selected r with Q fixed; external work assumes quasistatic transfer with no kinetic-energy change. No acceleration, radiation, polarization, finite-size charges, breakdown or dielectric response. Charge zero is a neutral ideal point with no polarization, not a general model of neutral matter.

Charge separation: 0.2 m Second charge: 2 nC

Reset keeps your prediction, captures and practice history.

Force, field, potential and interaction energy
Quantity	Value	Interpretation
Electric field from Q at q	449.500000 N/C	Rightward; defined even when q = 0
Force on q	0.899000 µN	qE; sign gives direction
Force on Q	-0.899000 µN	Equal-and-opposite partner on a different charge
Potential from Q at q	89.900000 V	Energy per charge; 1 V = 1 J/C
Pair interaction energy	0.179800 µJ	qV, with zero at infinite separation

Work from reference separation 0.20 m
Quantity	Value	Meaning
Reference potential	89.900000 V	From Q at 0.20 m
Initial pair energy	0.179800 µJ	Same q as selected now
Change in pair energy	0.000000 µJ	Final minus initial
Work by electric field	0.000000 µJ	Negative of interaction-energy change
Quasistatic external work	0.000000 µJ	Equal to energy change when kinetic energy does not change

The work comparison holds the selected q fixed between the reference and final positions. Changing the charge slider selects another scenario; it is not a simulated charging process. Supporting forces are omitted from the force-pair diagram, so its electric force values are not the total forces on the held charges.

repulsion: force on q 0.899000 µN; field from Q 449.500000 N/C to the right.

Potential from Q 89.900000 V; pair interaction energy 0.179800 µJ. From 0.20 m, field work 0.000000 µJ and quasistatic external work 0.000000 µJ. Changing q does not change the displayed field or potential from the prescribed Q.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

A location can have a field even with no probe charge

At 0.20 m to the right of Q = +2 nC, set q successively to +2 nC, −2 nC and zero. Predict which quantities change before capturing the results. The displayed field stays 449.5 N/C to the right. The force on q becomes +0.899 µN, −0.899 µN and zero respectively.

Electric field describes the force per positive test charge at a location. A positive charge feels force along the field; a negative charge feels force opposite it. A zero charge has zero force in this ideal model even where the source field is nonzero.

Connect source, field and response

The source Q produces E = kQ/r² on its right-hand side. Here E is the rightward field component in newtons per coulomb (N/C), k is the vacuum Coulomb constant, Q is source charge in coulombs, and r is distance in meters. Then F = qE gives the force component on a charge q placed there. Define each symbol before using it: Q and q refer to different charges.

For Q = 2 × 10⁻⁹ C and r = 0.20 m, E = (8.99 × 10⁹)(2 × 10⁻⁹)/0.040 = 449.5 N/C. Multiplying by q = −2 × 10⁻⁹ C gives F = −8.99 × 10⁻⁷ N. The coulombs cancel, leaving newtons.

One sometimes writes E = F/q for a nonzero test charge. At q = 0 that ratio is undefined; it does not establish that the source field is undefined. The separate source expression still gives 449.5 N/C. Distinguish an invalid way of measuring a quantity from absence of that quantity.

Read the field curve as a map of locations

The curve shows the field from Q at different positive positions, not a charge moving over time. Doubling r from 0.20 to 0.40 m reduces E to 112.375 N/C, one quarter as large. It also quarters force if q is unchanged. Changing q alone leaves this source-field curve unchanged.

These plots show only the field due to Q, excluding a charge’s field acting on itself. They are not a plot of the total two-source field everywhere. Real test charges can disturb a source distribution; the model prescribes Q and its location, so that redistribution is absent. The displayed neutral point does not polarize.

Use an unfamiliar field without needing the source formula

An independently specified uniform field points right with magnitude 200 N/C. What force acts on q = −3 nC? What if q is zero? This is a transfer problem; the browser’s source is still a point charge, whose field is not uniform.

Check the field transfer

F = (−3 × 10⁻⁹ C)(200 N/C) = −6 × 10⁻⁷ N = −0.6 µN, leftward. With zero q, force is zero while the prescribed field remains 200 N/C rightward. Neither result specifies a trajectory without mass, initial conditions and other forces.

In your reflection, explain how two probes at the same location can feel different forces while measuring the same undisturbed source field. Refer to signs and units, not only arrow color.

OpenStax: electric field explains field direction and the relation between field and force.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Explain the sign of F = qE and why F/q cannot be evaluated at q = 0 even though the source field is still defined.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Predict attraction and repulsion between charges Next: Connect voltage, interaction energy and electric work

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