Capacitance

Two conductors (any shape/geometry) connected to a voltage

$$ C = \Delta \frac{Q}{V} $$

Consider Parallel Plates:

$$ C = \frac{\epsilon A}{d} $$

Electrostatic Potential Energy

Electric potential energy per unit charge $q$

$$ V = \frac{q}{c} \newline W_e =\frac{1}{2}CV^2 \newline W_e = \frac{1}{2} \epsilon E^2 V $$

• Electrostatic Energy Density: $W_e = \frac{1}{2} \epsilon E^2$
• According to Coulomb’s Law, there is a force between positive and negative plates in the same direction of $\vec E$

$$ F_e = \frac{dW_e}{dz} $$