• Charge (q) on Parallel Plates

The charge stored on one plate in a two-plate arrangement is influenced by:

• Potential difference (V) between the plates.
• Area (A) of the plates.
• Separation (d) between the plates.

• The relationships are

  • q∝V (Direct relation with V)
  • q∝A (Direct relation with A)
  • q∝\(\frac 1d\)(Inverse relation with d)

• When combined: q =\(\frac {VA}{4πkd}\)

• Surface Charge Density (σ):
  It's like how packed the charge is on a plate! It's the charge (q) per unit area (A).

  • \(\frac qA\)​=\(\frac {V}{4πkd}\)​ orσ=\(\frac {V}{4πkd}\)​
  • Units of σ: Cm^-2 (Coulombs per square meter)

• Electric Field (E) between two parallel plates
  E = 4πkσ
  But wait, each plate is responsible for half, so for a single plate: E = 2πkσ

Imagine you're a tiny ant 🐜 and you get super close to a conductor's surface, say a sphere.

• From super close, the sphere looks flat, kinda like how Earth 🌎 seems flat until we see it from space!

• You'd see free electrons spaced equally. Why?

  • Each electron has forces from all others. They all balance out when the electron stops moving, meaning they're equally spaced.