⚡ Electric Charge & Field

Science Olympiad Circuit Lab — Topic 1 Study Guide

Division B · 2025–26 Season

1. What Is Electric Charge?

Key Definition

Electric charge (symbol: q or Q) is a fundamental property of matter that causes it to experience a force near other charged matter. Two types: positive (+) and negative (−).

Think of charge as a "tag" on particles. Protons carry +, electrons carry −, neutrons are neutral (no tag).

The Golden Rule

⟵ REPEL ⟶

−

⟵ REPEL ⟶

−

⟶ ATTRACT ⟵

−

"Opposites attract, likes repel." This shows up on EVERY test.

The Coulomb (C) — Unit of Charge

Key Numbers

1 coulomb = 6.24 × 10¹⁸ electrons (6.24 billion billion!)

One electron's charge: e = 1.602 × 10⁻¹⁹ C

Proton = +e | Electron = −e (equal magnitude, opposite sign)

💡 Scale

Carpet shuffle → ~1 μC (0.000001 C) on your body. Tiny!
Lightning bolt → ~5 C transferred in milliseconds. Enormous!

2. The Atom — Where Charge Lives

Protons & neutrons locked in the nucleus · Electrons orbit outside and can move

Particle	Charge	Location	Can Move?
Proton	+1.602 × 10⁻¹⁹ C	Nucleus	❌ No
Neutron	0	Nucleus	❌ No
Electron	−1.602 × 10⁻¹⁹ C	Orbiting	✅ Yes!

Key Insight

Only electrons move. "Positive charge" means it lost electrons. "Negative charge" means it gained electrons.

Never say something "gained positive charge." It lost electrons. Protons never leave the nucleus!

3. Three Properties of Electric Charge

① Quantization

Rule

Charge comes in discrete packets — always a whole-number multiple of e = 1.602 × 10⁻¹⁹ C.

q = n × e (n is any integer)

Example 1

Q: Is 4.806 × 10⁻¹⁹ C a valid charge?

n = 4.806×10⁻¹⁹ ÷ 1.602×10⁻¹⁹ = 3 ✅ Whole number → Valid!

Example 2

Q: Is 2.5 × 10⁻¹⁹ C a valid charge?

n = 2.5×10⁻¹⁹ ÷ 1.602×10⁻¹⁹ = 1.56 ❌ Not whole → Impossible!

② Conservation

Rule

Charge cannot be created or destroyed. Total charge in an isolated system is constant. Charge can only be transferred.

Example

Rub balloon on hair → balloon gains electrons (−), hair loses electrons (+).
Before: 0 total. After: (−x) + (+x) = 0. Still zero! ✅

③ Additivity

Rule

Net charge = algebraic sum of all individual charges.

Example

System: +3 C, −5 C, +2 C, +1 C
Total = 3 − 5 + 2 + 1 = +1 C

4. Conductors vs. Insulators

🔌 Conductors

Electrons flow freely. Outer electrons loosely bound.

Examples: copper, silver, gold, aluminum, salt water, human body

Resistance: Low

🧱 Insulators

Electrons blocked. Outer electrons tightly bound.

Examples: rubber, glass, plastic, wood, dry air, ceramic

Resistance: Very high

Metals = conductors, non-metals = insulators. Exception: graphite (carbon) conducts electricity.

Example

Q: Why do electricians wear rubber gloves?

Rubber is an insulator → blocks electron flow → prevents electric shock.

5. Static Electricity — Charges at Rest

Definition

Static electricity = buildup of electric charge on an object's surface. Unlike current electricity (flowing electrons), static charges stay put until they find a path to discharge.

Three Ways to Charge an Object

① Friction (Triboelectric)

Rubbing transfers electrons between materials.

📌 Balloon on hair → electrons jump hair→balloon. Balloon (−), hair (+).

② Conduction (Contact)

Touching a charged object to a neutral one shares charge directly.

📌 Charged rod touches metal sphere → both share charge.

③ Induction (No Contact!)

A charged object near a conductor rearranges charges inside without touching.

📌 Negative rod near metal sphere → electrons repelled to far side → near side (+), far side (−). Ground the far side → electrons escape to ground → remove rod → sphere is permanently (+)!

Induction: charge an object without ever touching it

Sources & Hazards of Static

Sources: Friction (walking on carpet, clothes dryer), separation of materials, flowing liquids/gases
⚡ Sparks: Can ignite flammable vapors, dusts, or gases (gas station danger!)
💻 ESD: Electrostatic discharge destroys sensitive electronics like computer chips
⚡ Lightning: Massive static discharge between clouds and ground

The #1 tested static hazard: "sparks that can ignite flammable vapors." That's why gas stations have grounding straps and "touch metal before refueling" signs.

6. Electric Fields — The Invisible Force Zone

Definition

An electric field (E) is the region around a charged object where other charges experience a force. Every charge creates a field extending into space.

Field Line Rules (Important!)

Lines point away from (+) charges and toward (−) charges
More lines = stronger field
Lines never cross
Lines are closer together where the field is stronger

Electric field lines: outward from positive, inward toward negative

Electric Field Formula

E = F / q

E = electric field strength (N/C or V/m) F = force on the test charge (Newtons) q = test charge (Coulombs)

You can also calculate the field from a single point charge:

E = k_e × Q / r²

k_e = 8.99 × 10⁹ N·m²/C² (Coulomb's constant) Q = source charge creating the field r = distance from the charge

Example

Q: A +2 μC charge creates an electric field. What is E at a point 0.5 m away?

E = k × Q / r² = (8.99 × 10⁹)(2 × 10⁻⁶) / (0.5)²
E = (8.99 × 10⁹)(2 × 10⁻⁶) / 0.25 = 17,980 / 0.25 = 71,920 N/C
Direction: away from the positive charge.

Think of it like gravity: A planet creates a gravitational field around it. Similarly, a charge creates an electric field around it. Other charges placed in that field feel a force — just like objects near a planet feel gravitational pull!

7. Coulomb's Law — The Math of Electric Force

The Big Formula

This is one of the most important equations for Circuit Lab. It tells you the force between two charged objects.

F = k_e × |q₁| × |q₂| / r²

F = electrostatic force between the charges (Newtons, N) k_e = Coulomb's constant = 8.99 × 10⁹ N·m²/C² q₁, q₂ = the two charges (Coulombs, C) r = distance between the centers of the charges (meters, m)

What Coulomb's Law Tells Us

Directly Proportional to Charges

Double one charge → force doubles.
Double both charges → force quadruples (4×).

Inversely Proportional to Distance²

Double the distance → force drops to 1/4.
Triple the distance → force drops to 1/9.
This is called an inverse-square law.

Worked Example 1

Q: Two charges, q₁ = +3 μC and q₂ = −5 μC, are 0.2 m apart. What is the force?

Given: q₁ = 3 × 10⁻⁶ C, q₂ = 5 × 10⁻⁶ C, r = 0.2 m
F = k × |q₁| × |q₂| / r²
F = (8.99 × 10⁹)(3 × 10⁻⁶)(5 × 10⁻⁶) / (0.2)²
F = (8.99 × 10⁹)(15 × 10⁻¹²) / 0.04
F = 0.13485 / 0.04 = 3.37 N
Direction: Attractive (opposite charges → they pull toward each other).

Worked Example 2 — Distance Change

Q: Two charges have a force of 12 N between them. If you double the distance, what's the new force?

Inverse square law: F ∝ 1/r²
Double distance → r becomes 2r → r² becomes 4r²
New force = 12 / 4 = 3 N
The force drops to one-quarter!

Worked Example 3 — Charge Change

Q: Two charges produce a force of 8 N. If you triple one of the charges, what happens to the force?

F ∝ q₁ × q₂ (directly proportional)
Triple one charge → force triples → 24 N

Watch out for the r² in the denominator! Students often forget to square the distance. If r = 0.3 m, you use 0.09, not 0.3.

Coulomb's Law looks just like Newton's Law of Gravity!
Gravity: F = G × m₁m₂/r² (masses attract)
Coulomb: F = k × q₁q₂/r² (charges attract OR repel)
Same shape, but gravity only attracts. Electric force can attract or repel!

8. Capacitance — Storing Charge

Definition

Capacitance is the ability to store electric charge. A capacitor is a device built specifically to do this — two metal plates separated by an insulating material (dielectric).

C = Q / V

C = capacitance (Farads, F) Q = charge stored (Coulombs, C) V = voltage across the capacitor (Volts, V)

1 Farad is HUGE — it means storing 1 coulomb for every volt. Real capacitors are usually measured in:

Prefix	Symbol	Value	Common Use
Microfarad	μF	10⁻⁶ F	Power supplies, audio circuits
Nanofarad	nF	10⁻⁹ F	Signal filtering
Picofarad	pF	10⁻¹² F	Radio, high-frequency circuits

Note: 100 nF = 0.1 μF (they're the same value, just different prefixes).

How a Capacitor Works

Two metal plates separated by an insulator. Charge builds up on the plates.

What Affects Capacitance?

Larger plate area → more capacitance (more room for charge)
Smaller plate gap → more capacitance (stronger electric field)
Better dielectric → more capacitance (insulator quality matters)

Worked Example

Q: A 100 μF capacitor is connected to a 9V battery. How much charge does it store?

C = Q / V → Q = C × V
Q = (100 × 10⁻⁶)(9) = 900 × 10⁻⁶ C = 900 μC = 0.0009 C

Worked Example

Q: A capacitor stores 0.005 C at 25V. What is its capacitance?

C = Q / V = 0.005 / 25 = 0.0002 F = 200 μF

Polarized vs. Non-Polarized Capacitors

Polarized (Electrolytic)

Has a + and − side. Must be connected correctly or it can be damaged/explode!

Examples: aluminum electrolytic, tantalum

Typical values: larger (1 μF to thousands of μF)

Non-Polarized (Ceramic/Film)

Can be connected either way — no polarity.

Examples: ceramic disc, film capacitors

Typical values: smaller (pF to low μF)

On the test, if they show a capacitor with a + marking, it's polarized. Connecting it backward can destroy it!

Think of a capacitor like a tiny rechargeable battery — but one that charges and discharges in fractions of a second. It stores energy temporarily, not long-term.

9. Real-World Hazards of Static Electricity

This is a frequently tested area. Know these scenarios!

Hazard	What Happens	Prevention
Gas station sparks	Static discharge ignites fuel vapors → fire/explosion	Touch metal (ground yourself) before pumping
ESD damage to electronics	Static zaps destroy tiny circuits in chips	Anti-static wrist straps, grounding mats
Grain elevator/dust explosions	Sparks ignite airborne dust particles	Grounding equipment, humidity control
Lightning	Massive charge buildup in clouds discharges to ground	Lightning rods (conductors that safely direct current to ground)
Surgical/hospital risks	Sparks near flammable anesthetic gases	Conductive shoes, grounded equipment

Key Takeaway

The common thread: static discharge (sparks) + flammable material = danger. Prevention always involves grounding — giving charge a safe path to flow away.

10. Key Person: Charles-Augustin de Coulomb

Historical Figure

Charles-Augustin de Coulomb (1736–1806) was a French physicist who discovered the law governing the force between electric charges.

Nationality: French
Era: 18th century
Famous for: Coulomb's Law — the inverse-square law of electrostatic force
Tool: Invented the torsion balance to precisely measure tiny forces between charged objects
Unit named after him: The coulomb (C) — the SI unit of electric charge
Key insight: Showed that electric force follows the same mathematical pattern as Newton's gravitational force (inverse-square law)

The test will ask which scientist is associated with the force between charges or the unit of charge. Answer: Coulomb. Don't confuse with Ampere (current), Ohm (resistance), or Volta (voltage).

11. Practice Problems (15 Questions)

Click "Show Answer" to check yourself. Try to solve each one before revealing!

Which of the following best describes Coulomb's Law?

A. The relationship between current and resistance
B. The force between two charges varies inversely with distance squared
C. Energy stored in a capacitor is proportional to its voltage squared
D. Magnetic flux is proportional to current

B. Coulomb's Law describes the force between two charges, which is inversely proportional to the square of the distance between them. F = kq₁q₂/r².

Which unit measures electric charge?

A. Volt B. Ampere C. Coulomb D. Ohm

C. Coulomb. Volts = voltage, Amperes = current, Ohms = resistance.

Which of the following best represents a hazard of static electricity?

A. Overheating of resistors
B. Sparks that can ignite flammable vapors
C. Excessive alternating current in circuits
D. Long-term capacitor leakage

B. The primary hazard of static electricity is sparks that can ignite flammable materials. This is why gas stations require grounding.

An object has 5 more protons than electrons. What is its charge?

Charge = n × e = 5 × 1.602 × 10⁻¹⁹ = +8.01 × 10⁻¹⁹ C (positive because more protons than electrons).

Two charges of +4 μC and −6 μC are 0.3 m apart. Calculate the force between them.

F = k|q₁||q₂|/r² = (8.99 × 10⁹)(4 × 10⁻⁶)(6 × 10⁻⁶) / (0.3)²
= (8.99 × 10⁹)(24 × 10⁻¹²) / 0.09 = 0.21576 / 0.09 = 2.40 N (attractive)

Two charges exert a force of 20 N on each other. If the distance between them is tripled, what is the new force?

F ∝ 1/r². Triple distance → force = 20 / 3² = 20 / 9 = 2.22 N

Define capacitance and give its SI unit.

Capacitance is the ability to store electric charge per unit voltage. SI unit = Farad (F). Formula: C = Q/V.

A rubber rod is rubbed with fur. The rod becomes negatively charged. Explain what happened using conservation of charge.

Electrons transferred from fur to rubber rod. Rod gained electrons (became −), fur lost electrons (became +). Total charge before = 0, total charge after = (−) + (+) = 0. Charge is conserved — it was only transferred, not created.

Electric field lines around a positive charge point:

A. Toward the charge B. Away from the charge C. In circles D. Randomly

B. Away from the charge. Field lines go FROM positive TO negative. For a lone positive charge, they radiate outward in all directions.

Q10

A 220 μF capacitor is connected to a 12V battery. How much charge is stored?

Q = CV = (220 × 10⁻⁶)(12) = 2,640 μC = 0.00264 C

Q11

Is a charge of 6.408 × 10⁻¹⁹ C possible? Why or why not?

n = 6.408 × 10⁻¹⁹ ÷ 1.602 × 10⁻¹⁹ = 4. Yes! It equals exactly 4 elementary charges. ✅

Q12

Which of the following is a conductor?

A. Glass B. Rubber C. Copper D. Plastic

C. Copper. It's a metal with loosely bound outer electrons. The others are all insulators.

Q13

Two identical metal spheres have charges of +8 μC and −2 μC. They are touched together and then separated. What is the charge on each sphere?

Total charge = +8 + (−2) = +6 μC. Since the spheres are identical, charge splits equally: +3 μC each. (Conservation of charge!)

Q14

Two charges produce a force of 10 N. If one charge is doubled AND the distance is halved, what is the new force?

F ∝ q/r². Double charge → 2×. Halve distance → 1/(½)² = 4×.
Combined: 2 × 4 = 8× original.
New force = 10 × 8 = 80 N

Q15

A capacitor stores 500 μC of charge when connected to a 10V source. What is its capacitance? If the voltage is increased to 20V, how much charge will it store?

C = Q/V = 500 μC / 10V = 50 μF
At 20V: Q = CV = 50 μF × 20V = 1000 μC (double the voltage → double the charge).

12. 📝 Cheat Sheet — Everything on One Page

Concept	Key Facts
Electric Charge	Property of matter. Two types: + and −. Like repels, opposite attracts. Unit: Coulomb (C).
Elementary Charge	e = 1.602 × 10⁻¹⁹ C. Proton = +e, electron = −e.
Quantization	q = n × e (charge is always a whole number of electrons).
Conservation	Charge cannot be created or destroyed — only transferred.
Conductors	Metals. Electrons flow freely. Low resistance.
Insulators	Non-metals (rubber, glass, plastic). Block electron flow.
Static Electricity	Charge buildup. Three methods: friction, conduction, induction.
Static Hazards	#1: Sparks igniting flammable vapors. Also ESD on electronics.
Electric Field	E = F/q = k×Q/r². Lines: away from (+), toward (−). Unit: N/C or V/m.
Coulomb's Law	F = k\|q₁\|\|q₂\|/r². k = 8.99 × 10⁹. Inverse-square law.
Capacitance	C = Q/V. Unit: Farad (F). μF, nF, pF for smaller values.
Capacitor	Two plates + dielectric. Stores charge. Polarized must be connected correctly!
Coulomb (person)	French physicist (1736–1806). Torsion balance. Discovered inverse-square law for charge.

Formula Quick Reference:
F = k|q₁||q₂|/r² (force between charges)
E = F/q = kQ/r² (electric field)
C = Q/V (capacitance)
k = 8.99 × 10⁹ N·m²/C² (Coulomb's constant)
e = 1.602 × 10⁻¹⁹ C (elementary charge)