Electrostatics — Easy Practice (Set 2)

Quick Recap — Dipole, Gauss, Potential & Capacitance

• Dipole: moment $p = q(2a)$; torque $\vec{\tau} = \vec{p}\times\vec{E}$; potential energy $U = -pE\cos\theta$.
• Gauss's law: total flux through a closed surface $\Phi = \dfrac{q_{enc}}{\varepsilon_0}$.
• Potential: $V = \dfrac{kq}{r}$ (a scalar, unit volt); $E = -\dfrac{dV}{dr}$; equipotential surfaces are perpendicular to field lines.
• Capacitance $C = \dfrac{Q}{V}$ (unit farad); a parallel-plate capacitor has $C = \dfrac{\varepsilon_0 A}{d}$, rising to $\dfrac{K\varepsilon_0 A}{d}$ with a dielectric.
• Energy stored: $U = \tfrac12 CV^2 = \tfrac12 QV = \dfrac{Q^2}{2C}$.