Electric Charge & Fields · Grade 12 Science

Chapter: Electricity, Magnetism & Circuits

Electric Charge & Fields

Learning goals

Readings for this unit

Before this unit

Charge signs and inverse-square interaction.

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Start with something to explain

Can a charge-free location still have an electric field?

Illustrative evidence case. A small test charge placed between remote sources experiences a force.

Charging changes an electron balance rather than creating chargeCharging changes an electron balance rather than creating charge−−−−−transfer 1 e⁻Before neutral → donor+e, receiver−e; total charge conserved.
Original selected-electron transfer model; omitted positive backgrounds are explicitly required for the neutrality account.

Notice and wonder

Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.

Can a charge-free location still have an electric field?

Your first model

Separate source charges, field at the location and force on the test.

Build the language from the idea

electric charge
A fundamental property of matter that comes in two types, positive and negative, measured in coulombs (C).
Coulomb's law
The rule that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance: F = kq₁q₂/r².
electric field
The region around a charge where another charge would feel a force; its strength is the force per unit charge, E = F/q, in N/C.
conductor
A material such as copper in which some electrons are free to move, so charge flows through it easily.
insulator
A material such as rubber or glass whose electrons are locked in place, so charge does not flow through it.

Everything you touch is built from atoms, and buried inside every atom is electric charge. Protons in the nucleus carry positive charge, electrons carry an equal-sized negative charge, and an atom with matching numbers of each is electrically neutral. Charge is quantized — it always comes in whole-number multiples of the elementary charge, e = 1.6 × 10⁻¹⁹ coulombs — so you can strip away three electrons or add a thousand, but never half of one. Charge is also conserved: it is never created or destroyed, only moved from one object to another. When you rub a balloon on your hair, you are not making charge, just transferring electrons from the hair to the balloon.

Charging changes an electron balance rather than creating chargeCharging changes an electron balance rather than creating charge−−−−−transfer 1 e⁻Before neutral → donor+e, receiver−e; total charge conserved.
Original selected-electron transfer model; omitted positive backgrounds are explicitly required for the neutrality account.

The single most important rule of charge is short: like charges repel, and opposite charges attract. Two negatives push apart, two positives push apart, but a positive and a negative pull together. This is strikingly different from gravity, which only ever attracts — electric forces come in both flavors, and that two-sidedness is exactly what makes circuits, chemistry, and electronics possible. It also explains everyday static electricity: a comb that has stolen electrons becomes negatively charged and can lift tiny bits of paper by attracting their positive regions.

Conductors have charge carriers that can move through the material under suitable conditions. Ordinary insulators strongly restrict sustained charge conduction but can still polarize, accumulate surface charge, leak, or break down at sufficiently large fields. Conducting versus insulating behavior depends on material, temperature, and operating conditions; it is not a claim that every electron is perfectly fixed or that an arbitrary insulating layer guarantees safe handling.

To go beyond 'they attract or repel' and actually predict the force, we use Coulomb's law: F = k·q₁·q₂ ÷ r², where the charges are in coulombs, the distance r is in meters, and the constant k ≈ 9 × 10⁹ N·m²/C². Two features matter most. Bigger charges mean a bigger force, in direct proportion. And because r is squared in the denominator, the force falls off fast with distance — double the separation and the force drops to a *quarter*, triple it and the force drops to a *ninth*. This inverse-square shape is the exact same mathematical fingerprint that Newton's law of gravitation carries, which is why the two laws are so often taught side by side.

Coulomb’s law needs geometry and force directionCoulomb’s law needs geometry and force direction++center separation rF = k|q₁q₂|/r²; direction follows charge signs.
Original two-positive-charge repulsion geometry; source sizes are schematic.

An electric field describes local force per sufficiently small positive test charge, E=F/q, in N/C. A source produces a field whether or not that test is present, and a negative test feels force opposite E. Field lines point away from positive and toward negative sources; their density can encode relative magnitude under a consistent drawing convention. Approximately uniform parallel-plate fields apply away from edge effects. Changes in sources propagate physically rather than implying instantaneous influence across arbitrary distances.

Electric field is defined independently of one test chargeElectric field is defined independently of one test charge+Field E points along the force on a positive test charge.
Original radial field directions for a positive point source; equal arrow lengths do not depict radial field magnitude decay.

These ideas are the bedrock of the entire unit and of modern technology. A moving stream of charge is nothing more than an electric current, the subject of the next lesson, and the push that drives it is a difference in electric potential built from these very fields. Electric fields steer the electrons that paint an old TV screen, sort the toner in a laser printer, trigger the spark in an engine, and register the touch of your finger on a phone. Learn to reason about charge, Coulomb's law, and fields, and you hold the key that unlocks everything from a single spark to the power grid.

Model check: Field exists as a model independent of the particular small test charge. F=qE=.002N along the field; a negative charge would reverse direction.

Build your understanding

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Part 1 · Account for charge and transfer

Electric charge is a signed property whose total is conserved in the selected complete system. In ordinary contact charging of solids, electrons can transfer while nuclei remain bound. A body that loses an electron becomes more positive; one that gains it becomes more negative. The dots here track selected electrons, not every particle in an initially neutral solid. Include the omitted positive background before interpreting net charge from the picture.

Charging changes an electron balance rather than creating chargeCharging changes an electron balance rather than creating charge−−−−−transfer 1 e⁻Before neutral → donor+e, receiver−e; total charge conserved.
Original selected-electron transfer model; omitted positive backgrounds are explicitly required for the neutrality account.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why does electron loss make a body more positive?

Visual reasoning — after your attempt

Its negative electron count falls while its positive nuclear charge remains, leaving a positive imbalance.

Electric charge can be positive or negative and is conserved in an appropriate complete system account. Ordinary charging often transfers electrons between materials; it does not create new protons inside atoms. A neutral object contains charges whose totals balance, not an absence of charged particles.

Removing electrons leaves a positive net charge. Induction can redistribute charge without immediate contact transfer, so distinguish separation from net addition.

Pause and explain

Does neutral mean there are no electrons?

Check your reasoning after answering

No. Neutrality means total positive and negative charge balance; charged constituents remain present.

Part 2 · Apply Coulomb’s law to a stated geometry

Coulomb’s law gives the electrostatic force magnitude between ideal point charges as k|q₁q₂|/r². Like signs repel and unlike signs attract along the joining line. Use center separation and compatible coulomb/meter units. Extended conductors can redistribute charge, so a single point-charge formula is not automatically valid for every charged object geometry. Equal opposite interaction forces act on the two different charges, consistent with Newton’s third law.

Coulomb’s law needs geometry and force directionCoulomb’s law needs geometry and force direction++center separation rF = k|q₁q₂|/r²; direction follows charge signs.
Original two-positive-charge repulsion geometry; source sizes are schematic.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

If separation triples with charges unchanged, what happens to force magnitude?

Visual reasoning — after your attempt

It becomes 1/9 as large under the point-charge model.

For point charges or suitable symmetric distributions, force magnitude is k|q₁q₂|/r². Direction follows attraction for opposite signs and repulsion for like signs. Use center separation and consistent units; extended nearby objects can need a more detailed charge-distribution account.

Doubling both charges multiplies force by four at fixed separation, while doubling separation divides it by four. Conditions determine the comparison.

Pause and explain

Why does the absolute-value formula not identify force direction?

Check your reasoning after answering

It calculates magnitude. Charge signs and geometry are still needed to assign the attraction or repulsion direction.

Part 3 · Distinguish field from force on a test charge

An electric field assigns force per positive test charge: E=F/q for a sufficiently small nonperturbing test. A positive source has outward field direction; a negative source has inward direction. A positive test charge feels force along E while a negative one feels force opposite E. Field units N/C differ from force units N. Field arrows are local direction indicators, not paths every released charge must follow.

Electric field is defined independently of one test chargeElectric field is defined independently of one test charge+Field E points along the force on a positive test charge.
Original radial field directions for a positive point source; equal arrow lengths do not depict radial field magnitude decay.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

If E points right, which way is force on an electron?

Visual reasoning — after your attempt

Left, because the electron’s charge is negative and F=qE.

Electric field describes force per positive test charge: E=F/q in a suitable small-test-charge limit. Its direction is the force direction for a positive charge. A negative charge experiences force opposite the field, so field arrows are not automatically force arrows for every particle.

The field near a negative source charge points toward it. A positive test charge accelerates toward the source, while a negative one is repelled.

Pause and explain

Does changing the test-charge sign reverse the source field?

Check your reasoning after answering

No. The field from the source is unchanged in the small-test approximation, but the force qE changes direction.

Part 4 · Add fields as vectors and inspect assumptions

Field superposition adds source-field vectors at the same location. At the midpoint of equal positive charges, equal opposite fields cancel even though neither source contribution is zero. Electric potential is a scalar sum and need not vanish there. Away from the symmetry point, calculate each distance and direction before combining components. A zero net field also does not mean that all nearby points have zero field or that arbitrary motion remains unchanged indefinitely.

A zero field can result from nonzero source contributionsA zero field can result from nonzero source contributions++Equal positive charges; midpoint fields cancel.Add vector fields at one location, not charge magnitudes alone.
Original symmetric midpoint field comparison; offset arrows show two alternative contributions at the same point.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

At this midpoint, is the field from each source individually zero?

Visual reasoning — after your attempt

No. Both are nonzero and equal in magnitude but opposite in direction.

Fields from multiple sources add vectorially in the usual electrostatic model. Equal source magnitudes do not guarantee cancellation at every point; directions and distances matter. A test charge large enough to redistribute source charges can alter the system and invalidate a simple fixed-source account.

Between equal like charges, fields cancel at the midpoint; between equal opposite charges, their midpoint fields reinforce.

Pause and explain

Why can equal charges give a nonzero combined field?

Check your reasoning after answering

Equal contributions can point in the same direction or arise at unequal distances. Vector geometry, not magnitude alone, determines the sum.

Apply the whole unit · Predict field and force from a negative source

Illustrative fixed source charge −3.00 μC and positive test charge +2.00 μC are 0.300 m apart in a vacuum point-charge model. Use k=9.00×10⁹ N·m²/C².

Your task

Calculate field at the test location and force on it, show their directions, and predict the effect of replacing the test charge with −2.00 μC without moving the source.

What your response should show

  • Define the system, quantities, units, and relevant conditions before selecting a model.
  • Show intermediate calculations or a labeled evidence account, including signs or denominators.
  • Explain how the supplied evidence supports the conclusion rather than reporting only an answer.
  • Identify a meaningful uncertainty, model limit, or measurement needed to test the conclusion.
Response guidance — after your attempt

  1. Source field magnitude=9.00×10⁹×3.00×10⁻⁶/0.300²=3.00×10⁵ N/C, toward the source.

  2. Positive-test force magnitude=2.00×10⁻⁶×3.00×10⁵=0.600 N, toward the source.

  3. With a negative test charge, field is unchanged but force points away, with the same magnitude.

The result distinguishes a source property at a location from the response of a selected charge. It assumes fixed point charges and a test charge that does not alter the source arrangement. A real conducting distribution may rearrange, so geometry and source constraints would need examination.

Scientific references and source-model foundations

Parent / teacher teaching notes

Ask students to draw field and test-force arrows separately. Require conversion of microcoulombs before substitution. Ask the learner to explain each symbol, axis, unit and arrow before calculating. Calculated examples, supplied illustrative records and actual historical observations are labeled separately. Selected public OpenSciEd middle-school source figures are foundation examples, not complete high-school editions or an endorsement; all advanced explanations are supplied locally.

A Bohr model of an atom showing a positively charged nucleus of protons and neutrons with negatively charged electrons orbiting around it.

Every atom holds positive protons in its nucleus and negative electrons around it — the source of all electric charge.

The key idea

Charge is quantized and conserved; like charges repel and opposites attract with a force given by Coulomb's law F = kq₁q₂/r²; every charge sets up an electric field E = F/q that points away from positive and toward negative charge.

Coulomb's Law

F = k·q₁·q₂ ÷ r²

F is the electrostatic force in newtons (N); q₁ and q₂ are the charges in coulombs (C); r is the separation in meters (m); k ≈ 9 × 10⁹ N·m²/C².

Electric Field Strength

E = F ÷ q

E is the electric field in newtons per coulomb (N/C); F is the force on a small test charge q. For a point charge this also equals E = k·q ÷ r².

Worked examples

Example 1

Find the electrostatic force between a +3 μC charge and a +4 μC charge separated by 0.6 m. (Use k = 9 × 10⁹ N·m²/C² and 1 μC = 1 × 10⁻⁶ C.)
  1. Write Coulomb's law: F = k·q₁·q₂ ÷ r².
  2. Substitute: F = (9 × 10⁹)(3 × 10⁻⁶)(4 × 10⁻⁶) ÷ (0.6)².
  3. The top is 9 × 10⁹ × 12 × 10⁻¹² = 0.108; divide by 0.36.
Answer: 0.3 N (repulsive, since both charges are positive)

Example 2 · Worked application

Two point charges have unchanged values but separation doubles. Compare Coulomb-force magnitudes.
  1. F=k×absolute(q₁q₂)/r².
  2. Replacing r by 2r increases the denominator fourfold.
  3. Direction depends on charge signs.
Answer: The force becomes one quarter as large.
Check the reasoning

Distance is center-to-center under the point-charge model.

Example 3

A small charge of 2 μC placed at a point feels an electric force of 0.3 N. What is the electric field strength at that point?
  1. Use the definition of electric field: E = F ÷ q.
  2. E = 0.3 ÷ (2 × 10⁻⁶).
  3. = 150,000.
Answer: 1.5 × 10⁵ N/C

Example 4 · Find and fix the mistake

Context: Two point charges have unchanged values but separation doubles. Compare Coulomb-force magnitudes. A student claims: “Electric field is the same quantity as the force on every test charge.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: Distance is center-to-center under the point-charge model.
  2. Field is force per unit positive test charge; actual force depends on test-charge value and sign.
Answer: Field is force per unit positive test charge; actual force depends on test-charge value and sign.
Check the reasoning

Distance is center-to-center under the point-charge model.

Example 5 · Reason from the visual model

Electric field is defined independently of one test chargeElectric field is defined independently of one test charge+Field E points along the force on a positive test charge.
Original radial field directions for a positive point source; equal arrow lengths do not depict radial field magnitude decay.
If E points right, which way is force on an electron?
  1. An electric field assigns force per positive test charge: E=F/q for a sufficiently small nonperturbing test. A positive source has outward field direction; a negative source has inward direction. A positive test charge feels force along E while a negative one feels force opposite E. Field units N/C differ from force units N. Field arrows are local direction indicators, not paths every released charge must follow.
  2. Left, because the electron’s charge is negative and F=qE.
Answer: Left, because the electron’s charge is negative and F=qE.
Check the reasoning

Original radial field directions for a positive point source; equal arrow lengths do not depict radial field magnitude decay.

Avoid these mistakes

Check your understanding

A+2microC test charge in 1000N/C field experiences what force?

Discuss the answer

F=qE=.002N along the field; a negative charge would reverse direction.

Return to the phenomenon

Return to the initial case. Can a charge-free location still have an electric field? Revise your drawing or explanation using two named ideas and one stated limitation.

Compare explanations after your attempt

Fields arise from sources elsewhere; force depends on test charge sign and magnitude, and fields combine as vectors.

What should we investigate next?

Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.

Investigate, calculate and revise

Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.

Activity 1 · Return to the opening case

Assigned reading and preparation

Use the opening phenomenon, unit definitions and explained Parts 1–4.

Your task

Return to the initial case. Can a charge-free location still have an electric field? Revise your drawing or explanation using two named ideas and one stated limitation.

Success criteria

  • Use the stated observations and appropriate units.
  • Connect a labeled model with the physical/environmental mechanism.
  • State assumptions and an evidence limitation.
  • Explain a substantive revision or next test.
Hint

Keep object/material identity, material transfer and energy account distinct.

Response guidance — discuss after your attempt

Fields arise from sources elsewhere; force depends on test charge sign and magnitude, and fields combine as vectors.

Activity 2 · Transfer to a changed case

Assigned reading and preparation

Cover the worked answer and use the explained models, relationships and notebook.

Your task

A+2 μC test charge in a uniform 500 N/C field points east. Find its force. What force acts on a−3 μC test at the same location?

Success criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
Hint

Name known quantities and conditions, show intermediate steps and check conservation.

Response guidance — discuss after your attempt

F=qE gives+0.0010 N east for+2 μC and−0.0015 N, i.e.west, for−3 μC. The field is unchanged in the ideal nonperturbing-test model.

Words to know

electric charge
A fundamental property of matter that comes in two types, positive and negative, measured in coulombs (C).
Coulomb's law
The rule that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance: F = kq₁q₂/r².
electric field
The region around a charge where another charge would feel a force; its strength is the force per unit charge, E = F/q, in N/C.
conductor
A material such as copper in which some electrons are free to move, so charge flows through it easily.
insulator
A material such as rubber or glass whose electrons are locked in place, so charge does not flow through it.

Coulomb weighed an invisible force with a twisted thread

How do you measure a force too weak to feel? In 1785, French engineer Charles-Augustin de Coulomb built a torsion balance: a light rod hung from a thin fiber, with a charged ball on one end. Bringing a second charged ball nearby made the rod twist, and the amount of twist revealed the force with astonishing precision. By varying the charges and distances, Coulomb showed the force is proportional to the product of the charges and falls off as the square of the distance — the inverse-square law we now write F = kq₁q₂/r². The unit of charge, the coulomb, is named in his honor, and the same delicate torsion-balance trick was later used to weigh the gravitational constant.

You can't have half an electron: Millikan's oil drops

The idea that charge is quantized — that it comes only in whole multiples of a smallest unit — was nailed down between 1909 and 1913 by Robert Millikan in his famous oil-drop experiment. He sprayed tiny charged oil droplets between two charged plates and balanced gravity against the electric force to measure the charge on each drop. Every charge he found turned out to be a whole-number multiple of the same tiny value, e ≈ 1.6 × 10⁻¹⁹ coulombs — the elementary charge. There simply were no in-between values. This is why you can transfer one electron or a billion, but never a fraction of one, and it earned Millikan the 1923 Nobel Prize in Physics.

Coulomb's law and Newton's gravity: identical shape, wildly different strength

Look at Coulomb's law and Newton's law of gravitation side by side and they are mathematical twins — both are inverse-square laws where the force depends on the product of two 'source' quantities (charge for one, mass for the other) divided by distance squared. But their strengths are worlds apart: between two electrons, the electric repulsion is about 10⁴² times stronger than their gravitational attraction. So why does gravity rule planets and galaxies while electricity seems to hide? Because matter is almost perfectly neutral — equal positive and negative charge cancel out over any large object — while mass only ever adds up. Gravity wins the cosmos by default, simply because charge cancels and mass never does.

Lightning is charge separation on a colossal scale

A thundercloud is a Coulomb's-law laboratory kilometers tall. Violent updrafts and colliding ice particles strip electrons from one region and pile them into another, separating enormous amounts of charge and building potential differences of hundreds of millions of volts between cloud and ground. When the electric field grows strong enough to rip electrons off air molecules, the air suddenly becomes a conductor and a lightning bolt discharges it all in a few thousandths of a second. Benjamin Franklin's famous (and extremely dangerous) 1752 kite work argued that lightning was simply electricity, and led directly to the lightning rod — a pointed conductor that quietly bleeds charge away and gives a strike a safe path to ground.

In the real world

Laser printers and photocopiers use Coulomb's law in action: a charged drum attracts oppositely charged toner powder exactly where the image should appear, then presses it onto the paper.

Exit check

A+2microC test charge in 1000N/C field experiences what force?

Check your explanation after answering

F=qE=.002N along the field; a negative charge would reverse direction.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

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