A = inside cavity with charge $+q$ → $E_A \neq 0$ (field lines from $+q$ to induced $-q$ on inner wall)
B and C = inside conductor material → $E_B = E_C = 0$ (electrostatic equilibrium)
Answer: $E_A \neq 0$, $E_B = E_C = 0$
(1) $E = 0$ inside conductor. (2) Net charge resides only on outer surface. (3) $E$ is perpendicular to surface just outside. (4) Surface is equipotential. (5) Charge distributes to maintain constant potential on surface. (6) At sharp points: high charge density, strong local E (corona discharge). For cavity inside conductor: inner surface has induced charge equal and opposite to enclosed charge; outer surface has charge = total charge on conductor + charge enclosed in cavity.
Gauss\'s law: $\oint \vec{E}\cdot d\vec{A} = Q_{enc}/\varepsilon_0$. For a Gaussian surface inside conductor (where E=0): $0 = Q_{enc}/\varepsilon_0$ → $Q_{enc} = 0$. This means: any charge inside a cavity must be exactly compensated by induced charge on inner surface. For spherical conductor: outside field = kQ/r^2 (point charge). Inside conductor: E = 0. Inside cavity with charge q: field due to q and induced charges.
Capacitance: $C = Q/V$ (charge per unit potential). Parallel plate: $C = \varepsilon_0 A/d$. With dielectric: $C = k\varepsilon_0 A/d$ where $k$ = dielectric constant. Spherical: $C = 4\pi\varepsilon_0 R$. Cylindrical: $C = 2\pi\varepsilon_0 L/\ln(r_2/r_1)$. Series: $1/C_{eq} = \sum 1/C_i$. Parallel: $C_{eq} = \sum C_i$. Energy: $U = \frac{1}{2}CV^2 = \frac{Q^2}{2C} = \frac{QV}{2}$.
Dielectric constant $k$ (or $\varepsilon_r$): ratio of capacitance with/without dielectric. Polarisation: dielectric molecules align with external field, creating internal field opposing external field. Net field inside dielectric: $E = E_0/k$ (reduced). Dielectric strength: maximum E before breakdown (dielectric constant for air $\approx 3\times10^6$ V/m). Polar molecules: have permanent dipole moment (water, HCl). Non-polar: dipole induced by external field (N2, O2).