Electric Charge and Electric Force
Introduced| English |
|---|
| electric force/ɪˈlektrɪk fɔːs/ |
| electric charge/ɪˈlektrɪk tʃɑːdʒ/ |
| coulombs/ˈkuːlɒmz/ |
| quantised/ˈkwɒntaɪzd/ |
| Coulomb's law/ˈkuːlɒmz lɔː/ |
| inverse-square law/ɪnˈvɜːs skweə lɔː/ |
| superposition/ˌsuːpəpəˈzɪʃn/ |
Why does a rubbed balloon stick to the wall?
- Rub a balloon on your hair and it clings to the wall — an invisible pull.
- That pull is the electric force 电力, one of the four fundamental forces.
- It acts between any objects that carry electric charge 电荷.
- This whole unit is built on one simple law for that force.
Two kinds of charge
- Charge comes in two kinds: positive and negative.
- Like charges repel; opposite charges attract.
- Charge is measured in coulombs 库仑 (C); the smallest free charge is the electron's, $e = 1.6\times10^{-19}$ C.
- Charge is quantised 量子化 (a whole number of $e$) and conserved — never created or destroyed.
Two negative charges are brought near each other. They:
Like charges repel — two negatives push apart.
Electric charge is measured in a unit called the ____.
Charge is measured in coulombs (C).
Coulomb's law
- The force between two point charges follows Coulomb's law 库仑定律.
- $F = \dfrac{k\,q_1 q_2}{r^2}$, with $k = 8.99\times10^9\ \text{N}\cdot\text{m}^2/\text{C}^2$.
- The force points along the line joining the two charges.
- Bigger charges give a bigger force; greater separation gives a weaker one.
Two $+3\ \mu\text{C}$ charges are $2\ \text{m}$ apart. Find the force (in N). Use $k = 9\times10^9$.
$F = \dfrac{(9\times10^9)(3\times10^{-6})^2}{2^2} = \dfrac{9\times10^9 \cdot 9\times10^{-12}}{4} \approx 0.02\ \text{N}$.
You double one of the two charges. The force between them:
$F \propto q_1 q_2$, so doubling one charge doubles the force.
An inverse-square law
- The $r^2$ on the bottom makes this an inverse-square law 平方反比.
- Double the distance and the force drops to a quarter.
- Triple the distance and it drops to a ninth.
- The very same $1/r^2$ shape returns later in gravity.
Coulomb's law
The force between two charges falls off with the square of their separation (an inverse-square law).
If you triple the distance between two charges, the force drops to one ninth.
Force goes as $1/r^2$, so $\times 3$ distance means $\div 9$ force.
Many charges add as vectors
- With several charges, find the force from each one on its own.
- Then add those forces as vectors — the superposition 叠加 principle.
- $\vec F_{\text{net}} = \sum \vec F_i$, added tip-to-tail.
- This lets us build the force from any arrangement of charge.
Select all true statements about the electric force.
Coulomb's law is inverse-square, along the join, and superposes. It attracts OR repels.
Two $+2\ \mu\text{C}$ charges sit $3\ \text{cm}$ apart. Find the force between them.
- $F = \dfrac{k\,q_1 q_2}{r^2} = \dfrac{(8.99\times10^9)(2\times10^{-6})^2}{(0.03)^2}$.
- $F \approx 40\ \text{N}$, and it is repulsive because both charges are positive.
Put the magnitudes of the charges into $F = k q_1 q_2 / r^2$, then decide the direction separately: repel for same signs, attract for opposite. Don't let a stray minus sign from a negative charge flip your force arrow the wrong way.
The electric force between two point charges obeys Coulomb's law $F = \dfrac{k\,q_1 q_2}{r^2}$ — an inverse-square law. Like charges repel, opposite charges attract, and the forces from many charges add as vectors (superposition).