Physics · Ch 1 — Electrostatics
Capacitors
Capacitors
The most common and simplest capacitor geometry is the parallel-plate capacitor: two identical flat conducting plates, each of area A, held parallel to each other and separated by a small distance d, with the region between them either empty (vacuum/air) or filled with a dielectric. When connected to a battery, one plate accumulates charge +Q and the other -Q, producing a pair of oppositely charged infinite (or, in practice, sufficiently large and closely spaced) sheets whose combined field, from section 1.6.4(iii), is uniform between the plates, with magnitude E = sigma/epsilon0 = Q/(epsilon0 A), and confined essentially entirely to the gap between the plates (negligible field exists outside the gap, ignoring edge effects). Since the field between the plates is uniform, the potential difference between them is simply V = E d = Q d/(epsilon0 A). The capacitance is then C = Q/V = epsilon0 A/d. This is the central formula for a parallel-plate capacitor: capacitance increases in direct proportion to the plate area A (larger plates can hold more charge at the same voltage) and decreases in inverse proportion to the plate separation d (bringing the plates closer together increases capacitance, since it strengthens the mutual attraction between the charges on the two plates for a given charge). Capacitors are manufactured in many different physical shapes and sizes -- including …
What this figure shows. A small photographic collage shows several real, commercially available capacitors of different physical construction and size -- disc-shaped ceramic capacitors, cylindrical electrolytic capacitors, and flat film capacitors among them -- illustrating that while the underlying physics (two conductors separated by a dielectric, storing charge proportional to voltage) is identical in every case, capacitors are manufactured in a wide variety of shapes, sizes and dielectri …
What this figure shows. Two identical flat conducting plates, each of area A, are drawn facing each other, separated by a small distance d, with the region between them either empty or filled with a dielectric; in the companion panel, a battery is shown connected across the two plates by wires, driving electrons off one plate (which becomes positively charged) and onto the other (which becomes negatively charged), building up equal and opposite charges +Q and -Q on the two plates until the potential difference between them exactly equals the batter …
What this figure shows. The uniform electric field lines running straight from the positive plate to the negative plate, filling the gap of separation d between them, are drawn with equal spacing (indicating uniform field strength E throughout the gap) and are shown ending abruptly (a fringing-field warning) near the plate edges, since the idealised uniform-field formula strictly holds only in the limit that the plate separation d is small compared with the plates' own linear si …