phys1702 w4 l1

Everything we touch: solids, liquids, and gases are made from atoms, which are built from many smaller particles. This comes from extensive scientific work in the 19th and 20th centuries.
Atoms have a central nucleus and electrons that live in the space around the nucleus.
The nucleus is not a simple blob; it is composed of smaller particles called protons and neutrons that are stuck together.
Different atoms have different numbers of protons and neutrons, which defines the type of atom (e.g., a lithium atom has 3 protons). The number of electrons in a neutral atom matches the number of protons.
For this discussion, the key takeaway is that matter is made of atoms, and atoms are built from protons, neutrons, and electrons.

Proton mass: m_p \,=\; 1.67\times 10^{-27} \ \text{kg} (written to three significant figures).
Neutron mass: slightly greater than the proton’s mass. When written to three significant figures, proton and neutron masses look the same; a difference only becomes evident if you use four significant figures.
Electron mass: m_e \,=\; 9.11\times 10^{-31} \ \text{kg}, which is much smaller than the proton or neutron mass.
Takeaway: among the three particle types (protons, neutrons, electrons), the electron is vastly lighter, while protons and neutrons are heavy by comparison.

Electric charge comes in two types: positive and negative.
Proton charge: q_p = +1.6\times 10^{-19} \ \text{C}, i.e., +E.
Electron charge: q_e = -1.6\times 10^{-19} \ \text{C}, i.e., -E.
Neutron charge: q_n = 0\ \text{C} (neutral).
The smallest unit of positive charge and the smallest unit of negative charge that can exist independently are both this elementary charge, denoted by the symbol E (often written as e in many texts). In SI units, E = 1.6\times 10^{-19} \ \text{C}.
Therefore, charges are commonly expressed as either +E (for protons) or -E (for electrons).
Summary of charge types:
- Proton: +E
- Electron: -E
- Neutron: 0
The elementary charge is the fundamental unit of electric charge that underpins all electrostatic interactions.

Charged particles exert electrostatic forces on each other; this is the electric analogue to gravitational attraction between masses, but with the crucial difference that electrostatic forces can be both attractive and repulsive depending on the charges.
Opposite charges attract: a positive and a negative particle exert an attractive electrostatic force on each other.
Like charges repel: two positive charges repel each other, and two negative charges repel each other.
Vectors of the forces obey Newton’s third law: the force that particle 2 exerts on particle 1 (denoted as F{12}) and the force that particle 1 exerts on particle 2 (denoted as F{21}) have the same magnitude but opposite directions, so |F{12}| = |F{21}| and the forces are directed along the line joining the two particles.

Define the forces:
- F_{12}: force on particle 1 due to particle 2.
- F_{21}: force on particle 2 due to particle 1.
Newton’s third law in this context implies equal magnitudes with opposite directions: |F{12}| = |F{21}| and the force vectors are opposite in direction along the line between the two particles.
Opposite charges case (one positive, one negative): these two particles attract each other.
- Example described: particle 1 (positive) and particle 2 (negative).
- Direction of forces:
- Force on particle 1 due to particle 2 is toward particle 2.
- Force on particle 2 due to particle 1 is toward particle 1.
Like charges case (both negative or both positive): these two particles repel each other.
- Example described: two negative particles (or two positive particles).
- Direction of forces:
- Force on particle 1 due to particle 2 is directly away from particle 2.
- Force on particle 2 due to particle 1 is directly away from particle 1.
In all cases, the magnitudes are equal (per Newton’s third law) even though the directions are opposite depending on the type of charges involved.

Scenario: opposite charges (one positive, one negative)
- Expectation: an attractive electrostatic force.
- Notation: F{12} points toward particle 2; F{21} points toward particle 1.
- Magnitudes: |F{12}| = |F{21}|.
Scenario: like charges (two negatives) or (two positives)
- Expectation: repulsive electrostatic force.
- Notation: each force points away from the other particle.
- Magnitudes: |F{12}| = |F{21}|.
Practical implications (bridging to real-world relevance)
- Electrical interactions underlie electricity, circuits, and many technologies.
- Understanding how charges attract or repel explains how atoms bond and how electrical forces operate at microscopic scales.
- The concept of the elementary charge and Coulomb's unit underpins measurements and calculations of forces between charged bodies.

Foundational model: atoms comprise a nucleus (protons + neutrons) and orbiting electrons; this structure explains why materials conduct electricity and how charges interact.
Physical laws involved:
- Masses of fundamental particles govern inertial properties and dynamics.
- Electric charge and electrostatic forces govern interactions between charged particles.
- Newton's laws (specifically Newton's third law) govern the action-reaction pair of forces between charges.
Real-world relevance:
- Electronics rely on behavior of electrons and their interactions with charged components.
- Understanding charge magnitudes and signs is essential for predicting attraction/repulsion in atomic bonds and in macroscopic devices.

Proton mass: m_p = 1.67 \times 10^{-27} \ \text{kg} (3 s.f.)
Neutron mass: slightly greater than the proton’s mass; difference becomes visible at higher precision (4 s.f. or more).
Electron mass: m_e = 9.11 \times 10^{-31} \ \text{kg}
Elementary charge: E = 1.6 \times 10^{-19} \ \text{C}
Charge types:
- Proton: +E
- Electron: -E
- Neutron: 0
Unit: Coulomb, symbolized by \mathrm{C}, the SI unit of electric charge.
Notation used in explanations:
- F_{12}: force on particle 1 due to particle 2.
- F_{21}: force on particle 2 due to particle 1.
Magnitude equality: |F{12}| = |F{21}|; directions are opposite for the action-reaction pair.

The dual nature of charge (positive vs negative) leads to both attractive and repulsive forces, enabling the rich array of phenomena from chemical bonding to electrical circuits.
The idea that only discrete elementary charges exist as the smallest unit underpins quantization in electrostatics and determines charge conservation in interactions.
The consistency of Newton’s third law in these microscopic interactions reinforces the universality of action l