Electrokinetics and Electrostatics

Electrokinetics: Charges and Fields

• Electrokinetics encompasses physicochemical and mechanical phenomena involving charge transport and effects of applied electric potentials.

• Electric charges (symbol q) are fundamental to various phenomena. They are measured in Coulombs (C), and can have positive or negative signs.

• Charges with the same sign repel, while opposite signs attract. Electrical neutrality describes a balance of positive and negative charges.

• The elementary charge (e) is 1.6 x 10^-19 C.

• Atoms comprise charged particles:

  • Electrons (e) with charge -1.6 x 10^-19 C and mass 9.1 x 10^-31 kg.
  • Protons (H+) with charge +1.6 x 10^-19 C and mass 1.67 x 10^-27 kg.

Electrostatics

• Electrostatics studies stationary electric charges.

• Electrification is the process of acquiring electric charge.

• Point charges are dimensionless, like material points in mechanics.

• Continuous charge distributions are macroscopic charges. Their infinitesimal charge (dq) is used in calculations.

• Charge density (linear, surface, volume) quantifies charge per unit length, area, or volume respectively.

Coulomb's Law

• Coulomb's law describes electrostatic force between stationary charges: Force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• qq'/4πε₀r² (Force equation).

• k = 1 / 4πε₀ = 9 x 10⁹ N⋅m²/C² (Coulomb's constant)

• Force is attractive if charges have opposite signs and repulsive if charges have the same sign.

Electrical Field

• The electrical field (E) is a vector quantity measuring the force on a positive test charge placed in the field. E = F/q.

• Its SI unit is N/C.

• The principle of superposition applies to electric fields, allowing calculation of net field from multiple charges.

Electric Potential

• Electric potential (V), measured in volts (V), is scalar, representing electrical potential energy per unit charge (U/q)

• The potential at a point due to a point charge Q is given by: V = Q / 4πε₀r.

• The electrostatic potential energy (U_E) of a point charge q at a point in the electric field due to a point charge Q is given by U_E = qQ /4πε₀r.

Conductors in Electrostatic Equilibrium

• Inside a conductor, the electric field is zero (E=0).

• The potential inside is constant; it's an equipotential volume

• All charges reside on the surface.

Capacitance

• The capacitance (C) of an isolated conductor is proportional to its charge (Q) and inversely proportional to its voltage (V). Q = CV.

• The SI unit of capacitance is the farad (F).

Capacitors

• A capacitor is a device utilizing two conductors (armatures) separated by an insulator (dielectric). Its capacitance depends on the geometry.

• Capacitance increases with the insertion of a dielectric medium (like glass, rubber, or air). C= kC_o, where k is the dielectric constant.

Electric Current and Current Density

• Electric current (I) is the ordered movement of charged particles (e.g., electrons, ions, holes). Measured in amperes (A).

• Current density (J). is the current per unit cross-sectional area of a conductor. J= I/A.

• In a conductor, the current depends on the applied voltage (Ohm's Law: V = IR).

Resistors

• Resistors oppose the flow of current within a circuit.

• Resistors can be connected in series or parallel; series resistance add linearly Req= Σ R_i While parallel resistance are calculated as 1/Req= Σ (1/R_i)

• The resistance depends on material characteristics .

Circuit Laws

• Kirchhoff junction rule: Σ I = 0 at any junction,.

• Kirchhoff's loop rule: Σ V = 0 around any closed loop.

Generators

• Generators provide the electrical power supply within a circuit.

• Voltage sources (e.g., batteries) provide a constant voltage regardless of current.

• Current sources provide a constant current regardless of voltage.

Wheatstone Bridge

• The Wheatstone bridge is a circuit for measuring unknown resistances.

• It utilizes the balance condition R₁/ R₂ = R₃/ R₄ to determine the unknown resistance (R) based upon known values for the other three resistors.