Electrostatics: Electric Charge and Coulomb's Law

• Electrostatics is the study of electric charges at rest
• It deals with the forces between charges, and the fields and potentials due to charges

Electric Charge

• Electric charge is a fundamental property of matter
• Charge is a conserved quantity, meaning the net electric charge in an isolated system never changes
• Charge is quantized and exists in discrete units of elementary charge (e), the charge of a single proton or electron
• The magnitude of e is approximately 1.602 × 10⁻¹⁹ Coulombs
• There exist two types of electric charge: positive (carried by protons) and negative (carried by electrons)
• Objects with the same type of charge repel each other
• Objects with opposite types of charge attract each other

Coulomb's Law

• Describes the electrostatic force between two point charges
• The force is directly proportional to the product of the magnitudes of the charges
• The force is inversely proportional to the square of the distance between the charges
• Coulomb's Law is expressed as: F = k * |q1 * q2| / r²
  • F is the electrostatic force
  • q1 and q2 are the magnitudes of the charges
  • r is the distance between the charges
  • k is Coulomb's constant, approximately 8.9875 × 10⁹ N⋅m²/C²
• The force is a vector quantity
• The direction of the force is along the line joining the two charges
• The force is attractive if the charges have opposite signs and repulsive if the charges have the same sign

Electric Field

• An electric field is a region of space around an electric charge in which another charge would experience a force
• The electric field (E) at a point is defined as the force (F) per unit positive charge (q₀)
• E = F / q₀
• Electric field is a vector quantity
• The direction of the electric field is the direction of the force on a positive test charge
• The electric field due to a point charge q at a distance r is given by: E = k * |q| / r²
• Electric field lines are used to visualize electric fields
• Electric field lines point away from positive charges and toward negative charges
• The density of electric field lines is proportional to the strength of the electric field
• Electric field lines never cross each other

Electric Potential

• Electric potential (V) is the electric potential energy per unit charge at a specific location in an electric field
• It is a scalar quantity
• The electric potential difference (ΔV) between two points is the work done per unit charge to move a charge between those points: ΔV = ΔU / q, where ΔU is the change in electric potential energy
• The electric potential due to a point charge q at a distance r is given by: V = k * q / r
• The electric field is related to the gradient of the electric potential, E = -∇V and in one dimension, E = -dV/dx
• Equipotential surfaces are surfaces on which the electric potential is constant
• Electric field lines are always perpendicular to equipotential surfaces
• No work is required to move a charge along an equipotential surface

Capacitance

• Capacitance (C) is a measure of a capacitor's ability to store electric charge
• A capacitor typically consists of two conductors separated by an insulator (dielectric)
• The capacitance is defined as the ratio of the charge (Q) stored on the capacitor to the potential difference (V) between the conductors: C = Q / V
• The unit of capacitance is the Farad (F), where 1 F = 1 C/V
• The capacitance of a parallel-plate capacitor is given by: C = ε₀ * A / d
  • ε₀ is the permittivity of free space (approximately 8.854 × 10⁻¹² F/m)
  • A is the area of each plate
  • d is the separation between the plates
• Energy stored in a capacitor: U = (1/2) * C * V² = (1/2) * Q * V = (1/2) * Q² / C

Dielectrics

• A dielectric is an insulating material placed between the plates of a capacitor
• Dielectrics increase the capacitance of a capacitor
• When a dielectric is inserted, the electric field within the capacitor decreases
• The dielectric constant (κ) is the factor by which the capacitance increases when a dielectric is inserted: C' = κ * C
  • C' is the capacitance with the dielectric
  • C is the capacitance without the dielectric
• A dielectric material becomes polarized when placed in an electric field
• Polarization involves the alignment of the molecules of the dielectric material in response to the field
• Dielectric strength is the maximum electric field that a dielectric material can withstand before breaking down

Electric Potential Energy

• Electric potential energy (U) is the potential energy of a charge q at a location with electric potential V
• U = q * V
• The change in electric potential energy (ΔU) when a charge q moves between two points with potential difference ΔV is: ΔU = q * ΔV
• The work done by the electric force when a charge moves between two points is equal to the negative change in electric potential energy: W = -ΔU
• For a system of two point charges, the electric potential energy is: U = k * q1 * q2 / r, where r is the distance between the charges
• The electric potential energy is positive if the charges have the same sign and negative if the charges have opposite signs

Conductors and Insulators

• Conductors are materials in which electric charges can move freely
• Metals are typically good conductors
• In conductors, there are many free electrons that can carry charge
• Insulators are materials in which electric charges cannot move freely
• Glass, rubber, and plastic are typically good insulators
• In insulators, electrons are tightly bound to atoms and cannot move easily
• When a conductor is placed in an electric field, the charges redistribute themselves on the surface of the conductor such that the electric field inside the conductor is zero
• The electric field at the surface of a conductor is always perpendicular to the surface

Charging Methods

• Charging by friction (triboelectric effect): Transfer of electrons between two materials when they are rubbed together, one material gains electrons and becomes negatively charged, the other loses electrons and becomes positively charged.
• Charging by conduction: Charging an object by direct contact with a charged object
• Charging by induction: Charging an object without direct contact
• Grounding: Connecting an object to the Earth to provide a path for charges to flow to or from the object e.g. removing excess charge

Explore electrostatics, the study of electric charges at rest, focusing on the fundamental properties of electric charge, including conservation and quantization. Learn about Coulomb's Law, which quantifies the electrostatic force between two point charges, detailing its direct proportionality to charge magnitudes and inverse square relationship with distance.