A neutral object loses electrons. What sign does its charge have?

Positive. Removing negative charge leaves an excess of positive charge.

What net force acts on a charge pushed equally in opposite directions?

Zero. Equal sizes cancel only because the force directions oppose each other.

At one point, two proposed field lines cross. What makes this drawing impossible?

Two directions at one point. A nonzero field has one direction, so its lines cannot cross.

A nonzero field runs parallel to a flat surface. What is its flux?

Zero. Only the perpendicular field component contributes.

Charges ±4 nC are 2 cm apart. What is their dipole moment’s magnitude?

8×10^-11 C m. Multiply one charge’s magnitude by the full separation.

What motion begins when a free dipole rests perpendicular to a uniform electric field?

Rotation. Opposite forces cancel overall but act at different ends.

If only the outside charge increases, what happens to net outward flux?

It stays unchanged. Only enclosed charge determines net outward flux, and that charge has not changed.

What field exists halfway between a uniformly charged spherical shell’s centre and its surface?

Zero. Spherical symmetry ensures cancellation throughout the empty interior.

Teach Electric Charges and Fields in eight steps.

For each idea: show it, ask before you tell, then say one line.

Gather paper and a pencil.

Common misconceptions & worked visual for this chapter · 15 practice questions with answers

Why it matters

Rubbed objects become charged because electrons move between them.
A charged comb attracts polarised paper because its field is uneven.
Electric attraction helps remove charged particles from factory exhaust.

What to teach

How to teach it

Charges, forces and fields

Neutral objects exchange one electron, leaving equal opposite charges and unchanged total charge.

1. Basic properties of electric charge

Electrons transfer whole charges; the combined charge stays unchanged.

Show: Follow the diagram’s electron transfer from A to B.
Ask: What charge will each object gain?
Say: A becomes positive; B becomes negative. Their total stays zero. Each electron transfers one elementary charge.
Used in: Earthing provides a conducting path for excess charge, reducing unwanted static sparks.

If your child says…“Positive charge means extra electrons.”

Ask: Which object lost negative charge?
What’s true: Gaining electrons makes an initially neutral object negative.

$F_L=0.90\,\mathrm N$

$F_R=0.225\,\mathrm N$

2. Coulomb’s law and superposition

Combine electric forces with their directions.

Show: Write these lines for three +1.0 μC charges in vacuum. Sources sit 0.10 m left and 0.20 m right of the target.
Ask: What net force acts?
Say: The opposing forces subtract, leaving 0.675 N rightward.
Used in: Electrostatic paint spraying attracts charged droplets towards a surface, reducing wasted paint.

If your child says…“I just add both force sizes.”

Ask: Does the right-hand charge help or oppose the left-hand charge’s push?
What’s true: Opposite forces subtract because they push in opposite directions.

Separate positive and negative charges with outward and inward field arrows.

3. Electric field and field lines

Fields determine electric forces; field lines show the field’s direction.

Show: Look at the diagram’s outward arrows around the positive charge. Find the inward arrows around the negative charge. Locate the marked point and follow its field arrow.
Ask: Which way would a positive test charge be pushed at this point?
Say: A positive test charge feels force along the arrow.
Used in: Electric fields drive charged exhaust particles towards collection plates, helping control industrial pollution.

If your child says…“Field lines cross where two fields meet.”

Ask: If lines crossed here, which single direction would the positive charge’s force take?
What’s true: A nonzero resultant field has one direction at each point.

Equal surfaces turn within a uniform field, with angles measured from their normals.

4. Electric flux

Flux measures how much electric field crosses a surface.

Show: Find the diagram’s normals, perpendicular to each surface.
Ask: Which orientation gives greatest flux?
Say: Flux is greatest along the normal.
Used in: Electric flux calculations help engineers choose insulation that reduces unwanted electrical sparks.

If your child says…“I measure the angle from the surface.”

Ask: When the field runs along the surface, how much points through it?
What’s true: The flux angle is measured from the surface normal.

Electric dipoles

Separated opposite charges produce rightward axial and leftward equatorial resultant fields.

5. Electric dipole moment and field

Separated opposite charges produce a direction-dependent field.

Show: Compare the diagram’s axial and equatorial field arrows.
Ask: Do these fields cancel?
Say: No: separated charges contribute differently.
Used in: Water’s separated charge centres help it dissolve salts, making salty deposits easier to wash away.

If your child says…“I use half the gap for the separation.”

Ask: Where does the distance between the charges begin and end?
What’s true: Dipole moment uses the full distance between the charges.

A tilted dipole has equal opposite forces producing a clockwise turning effect.

6. Dipole in a uniform electric field

Opposite forces can turn a dipole without accelerating its centre.

Show: Follow the diagram’s opposite force arrows.
Ask: Will these forces turn the dipole?
Say: Yes: equal opposite forces act at separate points. Their net force is zero.
Used in: Microwave ovens use changing electric fields to turn polar molecules, transferring energy that heats food.

If your child says…“Both forces add and push the dipole along.”

Ask: Do the opposite pushes act at the same place?
What’s true: The forces cancel overall but can produce rotation.

Charge distributions and Gauss’s law

A charged solid lies inside one boundary; an external charge’s field crosses another.

7. Continuous charge distribution and Gauss’s law

Enclosed charge sets net outward flux.

Show: Trace the diagram’s field crossings around each boundary.
Ask: Which boundary has positive net flux?
Say: The left boundary has positive net flux: net flux equals enclosed charge divided by epsilon zero.
Used in: Photocopiers control surface charge to attract toner where the printed image needs it.

If your child says…“The outside charge adds to net flux.”

Ask: Where does the outside charge’s entering flux leave?
What’s true: Only enclosed net charge sets the total outward flux through a closed surface.

Shell, wire and sheet with Gaussian surfaces showing where electric flux crosses.

8. Applications of Gauss’s law

Charge arrangement determines how fields vary.

Show: Compare the diagram’s Gaussian surfaces around the shell, infinite wire and infinite sheet.
Ask: What happens when distance doubles?
Say: The shell’s outside field quarters, the wire’s halves, and the sheet’s stays unchanged. Their different flux-crossing areas explain this.
Used in: Oppositely charged capacitor plates strengthen the field between them, helping store electrical energy.

If your child says…“Inside the shell, I use the point-charge field.”

Ask: What charge lies inside the smaller centred sphere?
What’s true: Spherical symmetry makes the shell’s field cancel everywhere inside.

A real problem

Electric forces collect particles from industrial exhaust.

Cottrell sought to control pollution from industrial smokestacks.

He applied for an electrostatic precipitator patent in 1907.

Charged exhaust particles are attracted to collection plates carrying the opposite charge.

National Inventors Hall of Fame US EPA

A factory chimney releasing smoky exhaust into the sky.

Concept Lab · Common misconception

The tempting mistake in Electric Charges and Fields

Open standalone misconception page →

Does zero enclosed charge mean zero field everywhere on a surface?

Wrong

If the net electric flux is zero, the electric field must vanish at every point of the surface.

Why it feels right. Gauss's law gives zero for the total, so I assign zero to every contribution.

Right

Flux sums signed contributions over the surface. Fields may cross it even when the sum is zero.

Worked example

Uniform field crosses both faces. Opposite outward normals make the flux contributions cancel.

Place a closed box in a uniform electric field.
Field enters one face and leaves the opposite face.
The contributions cancel although the field is present at both faces.

Ask your child eight quick questions.

One per step. The answer and the reason are given.

A neutral object loses electrons. What sign does its charge have?

Positive. Removing negative charge leaves an excess of positive charge.
What net force acts on a charge pushed equally in opposite directions?

Zero. Equal sizes cancel only because the force directions oppose each other.
At one point, two proposed field lines cross. What makes this drawing impossible?

Two directions at one point. A nonzero field has one direction, so its lines cannot cross.
A nonzero field runs parallel to a flat surface. What is its flux?

Zero. Only the perpendicular field component contributes.
Charges ±4 nC are 2 cm apart. What is their dipole moment’s magnitude?

$8\times10^{-11}$ C m. Multiply one charge’s magnitude by the full separation.
What motion begins when a free dipole rests perpendicular to a uniform electric field?

Rotation. Opposite forces cancel overall but act at different ends.
If only the outside charge increases, what happens to net outward flux?

It stays unchanged. Only enclosed charge determines net outward flux, and that charge has not changed.
What field exists halfway between a uniformly charged spherical shell’s centre and its surface?

Zero. Spherical symmetry ensures cancellation throughout the empty interior.

15 more questions with answers, 2 with pictures

Teach Electric Charges and Fields in eight steps.

Why it matters