07 / CHAPTER 05
Capacitance and dielectrics
Store electric energy and understand material response.
ANCHOR EQUATION
Capacitance
In symbols: C = Q/V
Capacitance measures charge stored per unit potential difference.
A capacitor stores field energy
A capacitor separates charge and stores energy in the electric field between conductors. Capacitance is geometry and material: it tells how much charge appears for a given potential difference.
Charge the plates incrementally
By definition C = Q/V. During charging, the potential rises with charge as V = q/C. The incremental work is dW = V dq = (q/C)dq. Integrating from 0 to Q gives U = ∫q/C dq = Q²/(2C) = ½CV². The energy resides in the field, not ‘inside’ the charge alone.
A 100 μF capacitor at 12 V stores U = ½(100×10⁻⁶)(144) = 7.2×10⁻³ J and holds Q = CV = 1.2 mC.
Voltage can be dangerous even at small energy
A high-voltage low-capacitance capacitor may store little total energy but still puncture insulation or startle a person. Dielectrics change C by polarizing and have breakdown limits.
Work it: A parallel-plate capacitor has area 0.02 m² and gap 1 mm in vacuum. Calculate C = ε₀A/d and energy at 100 V; check the units.