Grade 10

Advanced

7 min

Lesson 1 of 12

Electric Charge and Coulomb's Law

Not Started

Explores the fundamental nature of electric charges and the mathematical relationship governing the electrostatic force between them.

Have you ever wondered why a tiny plastic comb can defy gravity and lift pieces of paper? You are witnessing a force billions of times stronger than gravity, governed by the same invisible laws that hold your very atoms together.

Learning Objectives

1.Distinguish between charging by friction, conduction, and induction.
2.Calculate the electrostatic force between point charges using Coulomb's Law.
3.Explain the atomic behavior of electrons in conductors versus insulators.

The Mechanics of Charging

Everything around us is composed of atoms containing protons (positive) and electrons (negative). Usually, these are balanced, making objects neutral. However, we can move electrons to create a net charge. Friction occurs when two different materials rub together, physically 'knocking' electrons from one to the other. Conduction involves direct contact; electrons flow from a charged object to a neutral one to reach equilibrium. Finally, Induction is the most complex: a charged object is brought near a conductor (without touching), causing charges within the conductor to redistribute. If the conductor is then 'grounded,' it can gain a permanent net charge without ever having touched the original object.

Quick Check

If you bring a negatively charged rod near a neutral metal sphere and then touch the sphere with your finger (grounding it), what will be the final charge of the sphere?

Remember that induction causes like charges to move as far away as possible.

Answer

The sphere will become positively charged because electrons are repelled by the rod and flee into your finger (the ground).

Quantifying the Force: Coulomb's Law

In 1785, Charles-Augustin de Coulomb discovered that the force between two charges behaves much like gravity, but with a twist: it can both attract and repel. Coulomb's Law states that the electrostatic force

F

is directly proportional to the product of the charges

q_1

and

q_2

, and inversely proportional to the square of the distance

r

between them. The formula is:

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

where

k

is Coulomb's constant, approximately

8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2

. Because

r

is squared in the denominator, doubling the distance doesn't just halve the force—it reduces it to one-fourth of its original strength. This is known as an inverse-square law.

Calculate the force between two point charges of $+2 \times 10^{-6} \text{ C}$ and $-3 \times 10^{-6} \text{ C}$ separated by a distance of $0.5 \text{ m}$ .

1. Identify variables: $q_1 = 2 \times 10^{-6}$ , $q_2 = -3 \times 10^{-6}$ , $r = 0.5$ , $k = 9 \times 10^9$ . 2. Plug into formula: $F = (9 \times 10^9) \frac{(2 \times 10^{-6})(-3 \times 10^{-6})}{(0.5)^2}$ . 3. Simplify numerator: $(9 \times 10^9)(-6 \times 10^{-12}) = -0.054$ . 4. Divide by $r^2$ : $\frac{-0.054}{0.25} = -0.216 \text{ N}$ . 5. Interpretation: The negative sign indicates the force is attractive.

Conductors vs. Insulators: The Atomic View

Why does a copper wire carry electricity while a rubber glove stops it? It comes down to the valence electrons. In conductors (mostly metals), the outer electrons are loosely bound to their nuclei. They form a 'sea of delocalized electrons' that can move freely through the material. In insulators, electrons are tightly bound to specific atoms or molecules. They can shift slightly (a process called polarization), but they cannot flow. This is why induction works best on metals; the electrons have the freedom to migrate from one side of the object to the other in response to an external field.

Quick Check

Why is it impossible to charge a copper rod by friction while holding it in your bare hand?

Think about where the electrons go if they have a path to move.

Answer

Copper is a conductor; any charge transferred to the rod by friction will immediately flow through your body (also a conductor) to the ground.

Three charges are in a line. $Q_A = +4 \mu\text{C}$ is at $x=0$ , $Q_B = -2 \mu\text{C}$ is at $x=2\text{m}$ , and $Q_C = +4 \mu\text{C}$ is at $x=4\text{m}$ . What is the net force on $Q_B$ ?

1. Calculate $F_{AB}$ : $F = k \frac{(4 \times 10^{-6})(2 \times 10^{-6})}{2^2} = 0.018 \text{ N}$ (directed toward the left/negative x). 2. Calculate $F_{CB}$ : $F = k \frac{(4 \times 10^{-6})(2 \times 10^{-6})}{2^2} = 0.018 \text{ N}$ (directed toward the right/positive x). 3. Sum the forces: $F_{net} = -0.018 \text{ N} + 0.018 \text{ N} = 0 \text{ N}$ . 4. Conclusion: $Q_B$ is in electrostatic equilibrium.

Key Takeaways

1Charging occurs via the transfer of electrons, never protons.
2Coulomb's Law ( $F = k \frac{q_1 q_2}{r^2}$ ) shows that force decreases exponentially as distance increases.
3Conductors have free-moving electrons; insulators have tightly bound electrons.
4Induction creates a charge separation without physical contact.

Quick Check

Multiple Choice

If the distance between two charges is tripled, the electrostatic force becomes:

True/False

In a neutral atom, the number of protons always equals the number of electrons.

Multiple Choice

Which process requires a connection to the Earth to permanently charge an object?

What's Next?

Review Tomorrow

In 24 hours, try to sketch the process of induction from memory and write down Coulomb's Law formula.

Practice Activity

Find a plastic ruler and some small bits of paper. Rub the ruler on your sleeve and see how close you have to get before the paper jumps. This is the inverse-square law in action!

Browse

Browse

Electric Charge and Coulomb's Law

Learning Objectives

The Mechanics of Charging

Quantifying the Force: Coulomb's Law

Conductors vs. Insulators: The Atomic View

Key Takeaways

Quick Check

What's Next?

Electric Charge and Coulomb's Law

Learning Objectives

The Mechanics of Charging

Quantifying the Force: Coulomb's Law

Conductors vs. Insulators: The Atomic View

Key Takeaways

Quick Check

What's Next?