Electric Field Summary Table
| Region | Conductor | Uniform Insulator |
|---|---|---|
| r > R (outside) | E = kQ/ | E = kQ/ |
| r = R (surface) | E = kQ/ = σ/ε_{0} | E = kQ/ |
| r < R (inside) | E = 0 | E = kQr/ |
Capacitor Dielectric Modification Table
| Parameter | Battery Connected | Battery Disconnected |
|---|---|---|
| Fixed quantity | Voltage V | Charge Q |
| Capacitance | C → KC (×K) | C → KC (×K) |
| Charge | Q → KQ (×K) | Q → Q (unchanged) |
| Voltage | V → V (unchanged) | V → V/K (÷K) |
| Energy | U → KU (×K) | U → U/K (÷K) |
E vs r Graph Description:
- Conducting sphere: E = 0 for r < R; sharp jump to E = kQ/ at r = R; falls as 1/ for r > R
- Insulating sphere: rises linearly from 0 at center to kQ/ at surface; falls as 1/ outside
Conductor
Insulator (linear inside)
Dipole Field Direction:
- Axial field: parallel to dipole moment p (from −q to +q direction)
- Equatorial field: antiparallel to dipole moment p