⚡ Electric Charge and Coulomb's Law

Electric Charge

Electric charge is a fundamental property of matter that causes electromagnetic interactions.

Two Types:

• Positive (+): Protons
• Negative (-): Electrons

Key Properties:

1. Like charges repel, opposite charges attract
2. Charge is quantized: Comes in multiples of elementary charge $e = 1.60 \times 10^{-19} \text{ C}$
3. Charge is conserved: Total charge in isolated system is constant
4. Charge is invariant: Doesn't depend on reference frame

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Units of Charge

Coulomb (C): SI unit of electric charge

Elementary charge: $e = 1.60 \times 10^{-19}$ C

• Charge of proton: $+e$
• Charge of electron: $-e$

Any charge: $q = ne$ where $n$ is an integer

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Charging Methods

1. Friction (Triboelectric Effect)

• Rubbing transfers electrons
• Example: Rubbing balloon on hair

2. Conduction (Contact)

• Direct contact transfers charge
• Charge distributes between objects

3. Induction

• Charge separation without contact
• Grounding removes one type of charge

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Conductors vs. Insulators

Conductors

• Allow charges to move freely
• Examples: Metals, graphite, salt water
• Excess charge distributes on surface

Insulators (Dielectrics)

• Charges cannot move freely
• Examples: Rubber, glass, plastic, wood
• Charge stays where placed

Semiconductors

• Properties between conductors and insulators
• Examples: Silicon, germanium

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Coulomb's Law

Coulomb's Law gives the electrostatic force between two point charges:

$F = k\frac{|q_1 q_2|}{r^2}$

where:

• $F$ = electrostatic force (N)
• $k = 8.99 \times 10^9$ N·m²/C² (Coulomb's constant)
• $q_1, q_2$ = charges (C)
• $r$ = distance between charges (m)

Vector Form:

$\vec{F} = k\frac{q_1 q_2}{r^2}\hat{r}$

Direction:

• Same signs → repulsive (away from each other)
• Opposite signs → attractive (toward each other)

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Coulomb's Constant

$k = \frac{1}{4\pi\epsilon_0} = 8.99 \times 10^9 \text{ N·m}^2\text{/C}^2$

where $\epsilon_0 = 8.85 \times 10^{-12}$ C²/(N·m²) is the permittivity of free space.

Often approximated as: $k \approx 9.0 \times 10^9$ N·m²/C²

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Comparison with Gravity

Similarities:

• Both are inverse square laws: $F \propto 1/r^2$
• Both are long-range forces
• Both act along line connecting objects

Differences:

| Property | Gravity | Electricity | |----------|---------|-------------| | Always | Attractive | Attractive OR repulsive | | Constant | $G = 6.67 \times 10^{-11}$ | $k = 8.99 \times 10^9$ | | Relative strength | Very weak | Much stronger | | Shielding | No | Yes (conductors) |

Electric force is ~10³⁹ times stronger than gravity!

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Superposition Principle

For multiple charges, total force = vector sum of individual forces:

$\vec{F}_{total} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3 + ...$

Each force calculated using Coulomb's Law independently.

Steps:

1. Calculate force from each charge separately
2. Determine direction of each force
3. Resolve into components if needed
4. Add vectors (components)

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Problem-Solving Strategy

1. Draw diagram showing all charges and distances
2. Identify charge signs (+ or -)
3. Apply Coulomb's Law for each pair
4. Determine force directions:
   • Like charges → repel
   • Unlike charges → attract
5. Use superposition for multiple charges
6. Add as vectors (use components if needed)

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Common Mistakes

❌ Forgetting to square the distance in denominator ❌ Using wrong sign convention (use magnitude, then add direction) ❌ Not converting units (must use meters, coulombs) ❌ Adding forces as scalars instead of vectors ❌ Confusing force on A from B with force on B from A (equal magnitude, opposite direction)