# Electric Charge and Coulomb's Law

Physics I · Principles of Electromagnetism and Optics · https://tryals.app/learn/physics-i/electric-charge-and-coulombs-law

## Electric Charge and Properties

Rub a balloon on your hair and it picks up roughly $10^{-9}$ of its electrons’ worth of imbalance, enough to defy the gravity of the entire planet. Electricity is astonishingly strong; matter is just nearly perfectly neutral.

**Electric charge** is a fundamental property of matter. There are two types: **positive** and **negative**.

| Quantity | Symbol | SI Unit |
| --- | --- | --- |
| Charge | $q$ | C (coulomb) |
| Force | $\vec{F}$ | N (newton) |
| Permittivity | $\varepsilon_0$ | C$^{2}$/(N m$^{2}$) |

**Key properties of charge**:
- **Quantised:** $q = ne$ where $e = 1.602\times 10^{-19}$ C.
- **Conserved:** Total charge in an isolated system is constant.
- **Like charges repel, opposite charges attract.**

## Coulomb's Law and Force

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

$$\vec{F} = k_e\frac{q_1 q_2}{r^2}\hat{r}, \qquad k_e = \frac{1}{4\pi\varepsilon_0} = 8.99\times 10^9\;\text{N m}^2/\text{C}^2$$

**Superposition principle**: The net force on $q$ is the vector sum:

$$\vec{F}_{\text{net}} = \sum_i \vec{F}_i = \sum_i k_e\frac{qq_i}{r_i^2}\hat{r}_i$$

**Physics link:** Coulomb's law shares an inverse-square $1/r^2$ form with Newton's gravity, but electric forces can be attractive or repulsive.

**Common pitfall:** Coulomb’s law applies to **point** charges. For extended objects, you must integrate. You can only treat a sphere as a point at its centre due to a deep theorem, never by assumption.

## Practice questions

4 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. Two charges repel with **36 N**. You move them to **half** the original separation. Predict the new force.

**Answer:** 144 (within ±10)

**Why:** $36 \times 4 = 144$ N. The inverse-square law punishes proximity quadratically, the same geometry that makes gravity soar near massive bodies makes electrostatics fierce at atomic distances.

Page: https://tryals.app/practice/physics-i/electric-charge-and-coulombs-law/two-charges-repel-with-36-n-you-move-them-to-half-the-original

### 2. Match each charge-related concept to its description.

**Answer:**

- Elementary charge e → 1.6 $\times 10$⁻¹⁹ C
- Coulomb's constant k → 8.99 × $10^{9}$ $N\cdot m^{2}/C^{2}$
- Permittivity of free space $\varepsilon_{0}$ → 8.85 $\times 10$⁻¹² $C^{2}$/($N\cdot m^{2}$)
- Charge quantization → Charge comes in multiples of e

**Why:** These constants and principles underlie all of electrostatics.

Page: https://tryals.app/practice/physics-i/electric-charge-and-coulombs-law/match-each-charge-related-concept-to-its-description

### 3. Two charges repel with a force of **36 N**. You triple the distance between them. Predict the new force, in newtons.

**Answer:** 4 (within ±1)

**Why:** $36/9 = 4$ N. Inverse-square dilution is geometric: the same "influence" spreads over a sphere whose area grows as $r^{2}$, the same law gravity obeys.

Page: https://tryals.app/practice/physics-i/electric-charge-and-coulombs-law/two-charges-repel-with-a-force-of-36-n-you-triple-the-distance

### 4. Coulomb’s law and Newton’s law of gravitation have identical inverse-square form. What makes their predictions differ so profoundly?

A. The electric force falls off faster than the inverse square at large distances
B. Charge comes in two signs and mass in one, so gravity accumulates
C. Gravity acts only on matter while the electric force acts on all objects
D. Gravity acts instantaneously while the electric force propagates at $c$

**Answer:** B. Charge comes in two signs and mass in one, so gravity accumulates

**Why:** Cancellation is the whole difference. Bulk matter is electrically neutral, so the stronger force cancels itself out and the weaker one, which cannot cancel, runs the solar system.

Page: https://tryals.app/practice/physics-i/electric-charge-and-coulombs-law/coulombs-law-and-newtons-law-of-gravitation-have-identical