University:
Blinn College
Course:
PHYS 2426 | University Physics II
Academic year:

2025
Views:

301

Pages:

2
Author:

cam powell

Electrostatics and Circuits Notes Chapter 21: Electric Charge and Electric Field - Electric Charge Basics: Objects become charged by transfer of electrons; charge is quantized. - Conductors allow charge to move; insulators do not. Charge conservation holds. - Coulomb’s Law: F = k q1 q2 / r^2, with k = 1/(4??0). Force is along the line connecting charges; repulsive for like signs, attractive for opposite signs. - Electric Field Definition: E is force per unit positive test charge: E = F / q_test. - Field lines originate on positive charges and terminate on negatives; direction indicates force on a positive test charge. - Field of a Point Charge: For point charge Q at origin: E(r) = k Q / r^2 r_hat. Superposition: E = sum of fields from individual charges. - Field Lines and Visualization: Density indicates field strength; equipotential surfaces are perpendicular to field lines. - Conductors in Electrostatics: In equilibrium, E = 0 inside conductor; excess charge resides on surface. Induced charge: polarization and grounding effects. - Charging Methods: By contact or induction (grounding). Chapter 22: Gauss’s Law - Electric Flux and Gauss’s Law: Electric flux: ?_E = ? E · dA. Gauss’s Law: ? E · dA = Q_enclosed / ?0. - Choosing Gaussian Surfaces: Exploit symmetry: spherical, cylindrical, planar surfaces simplify integrals. - Applications: Point charge: E = (1/4??0) Q / r^2. Infinite line: E = ?/(2??0 r). Infinite plane: E = ?/(2?0). Coaxial cable: find E in regions rb using cylindrical surfaces. - Conductors and Cavities: Inside conductor, E = 0. Charge in cavity induces surface charges. - Non-symmetric Situations: Gauss's law always holds but may not yield analytic E without symmetry. Chapter 23: Electric Potential - Potential vs. Potential Energy: V(r) = U(r) / q_test, units volts (J/C). Potential difference ?V is work per unit charge. - Potential Due to Point Charges: V(r) = k Q / r (zero at infinity). Superposition for multiple charges. - Relation to Electric Field: E = -?V; equipotential surfaces perpendicular to E. - Potential Energy of Configurations: For two charges: U = k q1 q2 / r. For multiple, sum over pairs. - Examples: Compute potential at a point from multiple charges with signs and distances. - Applications: Work-energy relations, circuit voltage sources. Chapter 24: Capacitance and Dielectrics - Definition of Capacitance: C = Q / V, unit farad. - Parallel-Plate Capacitor: C = ?0 A / d; with dielectric: C = ? ?0 A / d. - Energy Stored: U = 1/2 C V^2 = 1/2 QV = Q^2/(2C). Energy density u = 1/2 ? E^2. - Networks of Capacitors: Series: 1/C_eq = ?1/C_i. Parallel: C_eq = ?C_i. - Dielectrics: Increase capacitance by ?; consider dielectric strength. - Capacitor Geometries: Cylindrical: C = 2?? L / ln(b/a). Spherical: C = 4?? ab/(b - a). Chapter 25: Current, Resistance, and Electromotive Force - Electric Current: I = dQ/dt, conventional current direction. - Microscopic View: I = n q v_d A; current density J = n q v_d; E = ? J. - Resistance and Resistivity: R = ? L / A; Ohm’s law: V = IR. - Electromotive Force (EMF): EMF provides work per unit charge; real sources have internal resistance: V_terminal = E - I r. - Power and Energy: P = IV = I^2 R = V^2 / R; energy W = P t. - Microscopic Models: Carrier density, temperature dependence of resistivity. - Applications: Transmission lines, resistive heating, circuit design. - Problem-Solving Tips: Compute R from ?, L, A; combine resistors; relate drift velocity; account for temperature.