🔋College Physics I – Introduction Unit 18 – Electric Charge and Fields

Key Concepts and Definitions

• Electric charge fundamental property of matter that causes it to experience a force when placed in an electromagnetic field
• Coulomb (C) SI unit of electric charge, equivalent to the charge transferred by a current of 1 ampere in 1 second
• Electric field region around an electrically charged particle or object in which an electric charge would experience a force
• Electric field strength magnitude of the electric field at a given point, measured in newtons per coulomb (N/C) or volts per meter (V/m)
• Electric potential energy potential energy that is stored in an electric field, measured in joules (J)
  • Depends on the charge and its position relative to the source of the electric field
• Electric potential difference in electric potential energy per unit charge between two points in an electric field, measured in volts (V)
• Electrostatic force attractive or repulsive force between electrically charged particles, governed by Coulomb's law

Fundamental Laws and Principles

• Conservation of electric charge total electric charge in an isolated system remains constant over time
  • Charges can be transferred between objects, but cannot be created or destroyed
• Superposition principle electric field at any point due to multiple charges is the vector sum of the electric fields produced by each charge individually
• Coulomb's law magnitude of the electrostatic force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them
  • $F = k \frac{|q_1q_2|}{r^2}$, where $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$)
• Gauss's law electric flux through any closed surface is equal to the total charge enclosed divided by the permittivity of free space ($\varepsilon_0$)
  • Relates the distribution of electric charge to the resulting electric field
• Electric field lines conceptual tool used to visualize the strength and direction of an electric field
  • Originate on positive charges and terminate on negative charges or at infinity
  • Field line density indicates the strength of the electric field

Types of Electric Charges

• Positive charge type of electric charge carried by protons and positively charged ions
  • Like charges (positive-positive or negative-negative) repel each other
• Negative charge type of electric charge carried by electrons and negatively charged ions
  • Opposite charges (positive-negative) attract each other
• Neutral objects with equal numbers of protons and electrons, resulting in a net charge of zero
• Induced charge redistribution of electric charges in a neutral object caused by the presence of a nearby charged object
  • Occurs through electrostatic induction, where the nearby charge causes the charges in the neutral object to separate
• Polarization alignment of electric dipoles (molecules with separated positive and negative charges) in response to an external electric field
  • Occurs in dielectric materials, which are insulators that can be polarized

Electric Fields and Their Properties

• Electric field direction direction in which a positive test charge would move when placed in the field
  • Points away from positive charges and towards negative charges
• Electric field magnitude strength of the electric field at a given point, determined by the force experienced by a unit positive test charge
• Uniform electric fields have a constant magnitude and direction throughout the region (capacitor plates)
• Non-uniform electric fields have a varying magnitude and/or direction in the region (point charges)
• Electric field lines visual representation of the electric field, with the direction of the lines indicating the field direction and the density of the lines indicating the field strength
• Superposition of electric fields electric field at a point due to multiple charges is the vector sum of the individual electric fields produced by each charge
• Shielding effect redistribution of charges in a conductor in response to an external electric field, resulting in a net electric field of zero inside the conductor

Coulomb's Law and Its Applications

• Coulomb's law states that the magnitude of the electrostatic force $F$ between two point charges $q_1$ and $q_2$ is directly proportional to the product of their charges and inversely proportional to the square of the distance $r$ between them
  • $F = k \frac{|q_1q_2|}{r^2}$, where $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$)
• Point charges idealized charged particles with no size or shape, used to simplify calculations
• Force direction like charges repel each other, while opposite charges attract each other
  • Direction of the force is along the line connecting the two charges
• Superposition principle net force on a charge due to multiple other charges is the vector sum of the individual forces exerted by each charge
• Electric field calculation electric field at a point due to a point charge can be found using $E = k \frac{q}{r^2}$, where $q$ is the source charge and $r$ is the distance from the source charge to the point of interest
• Limitations Coulomb's law is valid only for point charges and when the charges are stationary

Electric Field Calculations

• Electric field due to a point charge $E = k \frac{q}{r^2}$, where $q$ is the source charge, $r$ is the distance from the source charge, and $k$ is Coulomb's constant
  • Direction of the field is radially outward for positive charges and radially inward for negative charges
• Electric field due to a dipole combination of the electric fields produced by the positive and negative charges of the dipole
  • Field lines start from the positive charge and end on the negative charge
• Electric field due to a line of charge $E = \frac{1}{4\pi\varepsilon_0} \frac{\lambda}{r}$, where $\lambda$ is the linear charge density (charge per unit length) and $r$ is the perpendicular distance from the line of charge
• Electric field due to a charged plane $E = \frac{\sigma}{2\varepsilon_0}$, where $\sigma$ is the surface charge density (charge per unit area) and the field is perpendicular to the plane
  • Field direction is outward for positively charged planes and inward for negatively charged planes
• Superposition principle electric field at a point due to multiple charges is the vector sum of the individual electric fields produced by each charge
• Gauss's law relates the electric flux through a closed surface to the total charge enclosed, providing an alternative method for calculating electric fields in situations with high symmetry

Conductors and Insulators

• Conductors materials that allow electric charges to flow freely through them (metals)
  • Have a high density of free electrons that can move in response to an electric field
• Insulators materials that do not allow electric charges to flow freely through them (rubber, plastic)
  • Have a low density of free electrons and a large energy gap between the valence and conduction bands
• Semiconductors materials with electrical properties between those of conductors and insulators (silicon, germanium)
  • Can be made to conduct by adding impurities (doping) or by applying an external voltage
• Charge distribution in conductors electric charges in a conductor redistribute themselves to cancel out any external electric field inside the conductor
  • Charges accumulate on the surface of the conductor, creating an induced electric field that opposes the external field
• Shielding effect placing a conductor around an object can shield it from external electric fields, as the charges in the conductor will redistribute to cancel out the field inside
• Dielectrics insulators that can be polarized by an external electric field, resulting in a reduction of the electric field strength within the material
  • Polarization occurs due to the alignment of electric dipoles within the material

Practical Applications and Real-World Examples

• Electrostatic precipitators use electric fields to remove particulate matter from exhaust gases in industrial settings (power plants, factories)
  • Charged particles are attracted to oppositely charged plates, removing them from the gas stream
• Xerography (photocopying) process uses electric fields to transfer toner particles onto paper
  • A photoconductor is charged, selectively discharged by light, and then used to attract toner particles which are transferred to the paper
• Capacitors devices that store electric charge and energy in an electric field between two conducting plates
  • Used in a variety of electronic circuits for filtering, energy storage, and voltage regulation
• Van de Graaff generators use electrostatic induction to generate high voltages for scientific experiments and demonstrations
  • A moving belt transfers charge to a hollow metal sphere, creating a strong electric field around the sphere
• Electrostatic spray painting uses an electric field to atomize and direct paint particles onto a surface
  • The paint is charged as it passes through a high-voltage nozzle, causing it to be attracted to the grounded target object
• Lightning natural example of electric fields and discharge
  • Occurs when the electric field between a cloud and the ground or another cloud becomes strong enough to overcome the insulating properties of air
• Cathode ray tubes (CRTs) use electric fields to direct a beam of electrons onto a phosphorescent screen to create images (older television and computer monitors)
  • Deflection plates use electric fields to steer the electron beam and create the desired image