Electric Charges and Fields - Quick Revision
Charge
- Two kinds: positive and negative. Like charges repel, unlike attract.
- Properties: additive (scalars, add with sign), conserved (isolated system total fixed), quantised (q = n e, e = 1.6 x 10^-19 C).
- Conductors let charge move freely; insulators do not.
Coulomb's law
- F = k q1 q2 / r^2, k = 1/(4 pi epsilon0) = 9 x 10^9 N m^2 C^-2; epsilon0 = 8.854 x 10^-12 C^2 N^-1 m^-2.
- Vector, along the line joining charges; obeys Newton's third law and the superposition principle.
Electric field
- E = F/q (force per unit positive test charge), unit N/C. Point charge: E = k q / r^2, radial.
- Field lines: start on +, end on -; never cross; do not form closed loops; density shows strength.
Dipole (charges +q, -q a distance 2a apart; p = q x 2a, from -q to q)
- Axial field (r >> a): E = 2kp/r^3 (along p). Equatorial: E = kp/r^3 (opposite p). Dipole field falls as 1/r^3.
- In a uniform field: net force zero, torque tau = p x E, magnitude pE sin theta.
Flux and Gauss's law
- Flux: Phi = E.S = E S cos theta, unit N m^2 C^-1 (= V m).
- Gauss's law: closed-surface flux = q_enclosed / epsilon0.
- Line charge: E = lambda/(2 pi epsilon0 r). Infinite sheet: E = sigma/(2 epsilon0). Shell: E = kq/r^2 outside, 0 inside.