Electrical Forces

Fundamental Forces

  • The universe operates under the influence of four fundamental forces. These forces are crucial to understanding how physical interactions occur across various scales.

  • Gravity has been studied in detail, but it is essential to note that friction is not a fundamental force; it is a result of more fundamental forces.

  • The four fundamental forces include: strong nuclear force, electromagnetic force, weak nuclear force, and gravity.

Fundamental Forces Overview

Strong Nuclear Force

  • Strength: Very strong

  • Range: Approximately 1 × 10^-15 meters (diameter of a medium-sized nucleus)

  • Particles Mediating Force: Gluons

  • Function: Holds the nucleus together by acting between nucleons (protons and neutrons).

Electromagnetic Force

  • Strength: Strong (but weaker than the strong nuclear force)

  • Range: Infinite

  • Particles Mediating Force: Photons

  • **Properties: ** Mass of photon = 0, Spin = 1

Weak Nuclear Force

  • Strength: Intermediate strength

  • Range: Very short (about 10^-18 meters, around 0.1% of a proton's diameter)

  • Particles Mediating Force: W and Z bosons

  • Function: Induces beta decay and interacts with neutrinos. Mass > 80 GeV, Spin = 1.

Gravity

  • Strength: Extremely weak

  • Range: Infinite

  • Particles Mediating Force: Gravitons (hypothetical)

  • Properties: Mass = 0, Spin = 2

The Electrical Force

  • Electricity introduces charges as a main property of matter, akin to gravitational mass.

  • There are two types of charge: positive and negative. These are arbitrary labels with mathematical utility.

Charge Fundamentals

  • Measurement of charge is in coulombs (1 C).

  • Charges exert forces on other charges:

    • Like charges repel each other.

    • Opposite charges attract each other.

Atomic Structure

  • Atoms consist of a nucleus surrounded by electrons.

  • Nucleus: Contains protons (positive charge) and neutrons (neutral charge).

  • Electrons: Negatively charged particles surrounding the nucleus.

Charge of Subatomic Particles

  • Protons: Charge of approximately +1.602 × 10^-19 C, known as the elementary charge (denoted as +e).

  • Neutrons: No charge; neutral.

  • Electrons: Charge approximately -1.602 × 10^-19 C (denoted as -e).

Fundamental Particles

  • Electrons: Basic units of electrical charge, not composed of smaller units.

  • Protons and Neutrons: Composed of quarks.

  • Quarks: Fundamental particles with several types; protons: 2 up-quarks and 1 down-quark; neutrons: 2 down-quarks and 1 up-quark.

Charge Calculations

  • Question: Calculate the charge of up-quarks and down-quarks based on the proton's and neutron's charge composition.

  • Proton: 2 up-quarks (+1) + 1 down-quark (charge calculated to achieve a net +1).

  • Neutron: 2 down-quarks + 1 up-quark (charge calculated to achieve a net of 0).

Coulomb’s Law (Vacuum)

  • Coulomb's Law describes the force (F) between two charges ( Q1 and Q2) in a vacuum:

[ F = \frac{1}{4 \pi \varepsilon_0 } \frac{Q1 \times Q2}{r^2} ]

  • Variables:

    • [ Q1, Q2 ] : charges

    • [ r ] : distance between charges

    • [ \varepsilon_0 ] : permittivity of free space (approximately 8.854 × 10^-12 F/m).

  • This equation resembles Newton’s Law of Universal Gravitation since both exhibit an inverse square relationship.

  • Negative forces are attractive.

Gravity and Charge Forces

  • For gravity:

[ F = G \frac{M1 \times M2}{r^2} ]

Attractive and Repulsive Forces

  • The sign of the force varies:

    • Attractive Force (negative): When charges have opposite signs

    • Repulsive Force (positive): When charges have the same signs

Coulomb’s Law - Examples

Example 1

  • Calculate the force between charges Q1 = +2 C and Q2 = -3 C, 3 meters apart:

  • The calculated force, [ F = -5.99 \times 10^9 N ]; indicating a strong attractive force.

Example 2

  • Calculate the force between charges Q1 = -3 C and Q2 = -4 C, 20 meters apart:

  • The resulting force, [ F = +2.7 \times 10^8 N ]; highlighting a strong repulsive force.

Coulomb’s Law with Dielectric

  • If non-conductive media (dielectric) is present, electrostatic force decreases by a constant factor ( \varepsilon_r ) (relative permittivity), which varies by material.

  • For example, water has ( \varepsilon_r \approx 80 ).

Coulomb’s Law (Full Equation)

  • The complete equation incorporating dielectric:

[ F = \frac{1}{\varepsilon_0 \varepsilon_r} \frac{Q1 \times Q2}{r^2} ]

Example 3

  • Calculate the force between charges Q1 = +2 C and Q2 = +1 C, 10 meters apart in water:

  • Resulting force: [ F = 2.25 \times 10^6 N ]; a substantial repulsive force.

Example 4

Part (i)

  • Calculate electric force between 2 up-quarks in a proton (distance: 1 × 10^-16 m, charge of up quark = ⅔ e):

Part (ii)

  • Resulting force calculation yields [ F = 1.025 \times 10^4 N ]; indicating strong repulsion, which is counteracted by the strong nuclear force keeping the nucleus stable.