Fundamental Interactions and Electric Charges

The Fundamental Interactions of the Standard Model

• The Standard Model of particle physics includes four fundamental interactions:

  • Gravity (8A)

  • Electromagnetism (8B)

  • Acts over a distance without contact.

  • Decreases with increasing distance.

  • Force can be either attractive or repulsive.

  • Weak Interaction (8C)

  • Strong Interaction (8C)

Electric Charges and Fields

• Study materials referenced:

  • OpenStax – University Physics Volume 2 Chapter 5

  • Serway|Jewett – Physics for Scientists and Engineers Chapter 23

Preview Problems

1. Point Charge Problem

   • Given:

     • Charge A: 7.50 nC

     • Charge B: 4.20 nC

     • Distance: 1.80 m

   • Task:

     • Calculate the electric force between the charges and determine the nature (attractive or repulsive) of this force.

2. Continuous Line of Charge

   • Line extends from 𝑥 = 𝑥0 to positive infinity, uniformly carrying positive charge density 𝜆.

   • Task:

     • Find the electric field vector at the origin.

3. Speed Calculation in Electric Field

   • An electron and a proton released from rest in a field of 520 N/C.

   • Calculate their speeds after 48.0 ns.

4. Electric Field and Circular Loop

   • Circular loop: 40.0 cm diameter rotated in a uniform electric field.

   • Maximum electric flux: 520 kN·m²/C.

   • Task:

     • Determine the magnitude of the electric field.

5. Average Volume Charge Density

   • Electric field at 500 m: 120 N/C downward; at 600 m: 100 N/C downward.

   • Task:

     • Calculate average volume charge density between elevations and determine sign.

6. Tension in Conducting Wire

   • Two spheres (radius: 0.500 cm) connected by a 2.00 m wire, one carrying a charge of 60.0 mC.

   • Task:

     • Determine tension in the wire.

A Brief History of Static Electricity and the Electric Force

• Thales of Miletus (624-546 BCE): Studied amber and rabbit's fur.

• William Gilbert (1544-1603): Investigated rock crystals and gemstones.

• Charles du Fay (1698-1739): Proposed two types of electric fluids:

  • Vitreous

  • Resinous

• Benjamin Franklin (1706-1790): Introduced the concept of a single electric fluid, defining excess as positive (vitreous) and deficiency as negative (resinous).

Electric Force: Observations & Properties of Charge

• The electric force has several key characteristics:

  • Acts without physical contact.

  • Can be attractive or repulsive.

  • Not all objects are influenced by electric forces.

  • The strength of the force decreases with distance.

Electric Charges

• Fundamental properties of electric charges include:

  • Quantized: Charges exist only in discrete amounts, regardless of type or sign.

  • Conserved: Charge is conserved universally and locally.

  • Defined as a property, not a particle, with the SI unit of measurement being Coulombs (C).

Charge Source and Atomic Structure

• Elementary charge

  • Negative electron charge (q_e^- = -1.602176634 imes 10^{-19} C)

  • Positive proton charge (q_p^+ = +1.602176634 imes 10^{-19} C)

  • Neutral neutron charge (q_n^0 = 0 C)

Conductors, Insulators, and Semiconductors

• Conductors: Materials that allow free movement of electric charge.

  • Examples: Metals, ionic solutions with free electrons.

• Insulators: Materials that do not allow free movement of charge.

  • Examples: Wood, rubber, glass, which have bound electrons.

• Semiconductors: Materials that can exhibit properties of both conductors and insulators depending on their impurity content.

  • Examples: Silicon, germanium, gallium arsenide.

Polarizing by Induction

• Inductions categorize how charges on objects can influence each other without contact.

Coulomb’s Law

• The relationship between electrical force, charge, and distance:

  • F ext{ (Electric Force)} ext{ between two point charges }

  • Electromagnetic interaction is described as:

  • F ext{ (Electromagnetic)} ext{ is proportional to } rac{Qq}{r^2}

  • F = ke rac{Qq}{r^2} ext{ (with } ke = 8.99 imes 10^9 N ext{ m}^2/C^2)

  • Inverse Square Law: The relationship where force decreases with increasing distance.

Example Problem: Ratios of Forces in Hydrogen Atom

• A hydrogen atom comprises one proton (mass: m{p^+} = 1.67 imes 10^{-27} ext{ kg} with charge qp^+) and one electron (mass: m{e^-} = 9.11 imes 10^{-31} ext{ kg} with charge qe^-).

• Ratio of electric force to gravitational force:

  • rac{FE}{FG} = rac{Fq}{Fm} with gravitational force given by Newton's Law of Gravitation: F_G = G rac{Mm}{r^2} and electric force as per Coulomb’s law.

Superposition of Electric Forces

• Superposition principle allows calculation of net force from multiple point charges:

  • For point charges F_{1} = ext{sum of all interactions with charge 1}

  • F{1} = igg( rac{q1q2}{r{12}^2} igg) + igg( rac{q1q3}{r{13}^2} igg) + igg( rac{q1q4}{r{14}^2} igg)

Charge Motion in Electric Fields

• Equation of Motion in a Uniform Electric Field

  • FE = ma where FE: Electric ext{ Force}; m: mass; a: acceleration.

  • Motion in a uniform electric field shows the same acceleration principles as motion in gravitational fields, modeled accurately by vectors.

Electric Dipoles

• Defined as a pair of equal and opposite charges separated by a distance d.

• Electric Dipole Moment: p = q imes d.

• Electric dipoles experience torque in an electric field given by the equation: au = p imes E (where au is torque and E is the electric field).

Electric Field Lines

• Visual representation of electric fields that start from positive charges and end at negative charges.

• Number of lines corresponds to the charge's magnitude, indicating directionality and strength of the field.

• Rules: Lines can never intersect, a characteristic of vector fields.