The electric flux through any closed surface is proportional to the enclosed electric charge.
Applies to symmetric charge distributions for easy calculation of electric fields.
Applications:
Spherical symmetry (point charge, sphere).
Cylindrical symmetry (infinite wire).
Planar symmetry (infinite sheet).
Lesson 6: Conductors in Electrostatics
Key Properties:
E = 0 inside a conductor in electrostatic equilibrium.
Excess charge resides on the surface of a conductor.
The surface of a conductor is an equipotential.
The electric field just outside a conductor is perpendicular to the surface with magnitude \sigma / \epsilon_0, where \sigma is the surface charge density.
Shielding:
Conductors block external electric fields.
Used in Faraday cages to protect sensitive equipment from external electric fields.
Lesson 7: Capacitors
Capacitance:
C = \frac{Q}{V}, where C is capacitance, Q is the charge stored, and V is the potential difference.
Unit: Farad (F).
Parallel Plate Capacitor:
C = \epsilon_0 \frac{A}{d}, where A is the plate area and d is the distance between the plates.
Energy Stored:
U = \frac{1}{2} CV^2 = \frac{1}{2} QV = \frac{1}{2} \frac{Q^2}{C}
Dielectrics:
Inserting a dielectric increases capacitance.
C' = K C, where K is the dielectric constant.
Lesson 8: Electric Dipoles
Definition:
Two equal and opposite charges (+q and -q) separated by a distance d.
Dipole moment:
\vec{p} = q \vec{d}, where \vec{p} is the dipole moment vector, pointing from the negative charge to the positive charge.