| Electric field and potential | |
| Coulomb's law: | F12 = (keq1q2/r122) (r12/r12). |
| Electrostatic field of a point charge: | E = (keq/r2)(r/r). |
| Gauss' law: | Φe(through closed surface) = Qinside/ε0. |
| Electrostatic potential energy: | ∆U = UB - UA = -q ΣAB E∙∆r. |
| Electrostatic potential difference: | ∆V = ∆U/q |
| The potential of a point charge: | V(r) = kq/r (convention: V = 0 at infinity.) |
| Field and potential: | Ex = -∆V/∆x, Ey = -∆V/∆y, Ez = -∆V/∆z |
| Capacitors | |
| Capacitance: | C = Q/V |
| Parallel plate capacitor: | C = εA/d |
| Energy stored in a capacitor: | U = ½(Q2/C) = ½CV2 |
| Capacitors in series | 1/C = (1/C1) + (1/C2) + (1/C3) |
| Parallel capacitors: | C = C1+ C2 + C3 |
| Currents and circuits | |
| Current: | I = ∆Qnet/∆t = j∙A, j = current density |
| Resistance: | R = ∆V/I |
| Resistance of a straight wire: | R = ρL/A |
| Power: | P = I∆V = I2R = (∆V)2/R |
| Resistors in series: | R = R1 + R2 + R3 |
| Parallel Resistors: | 1/R = (1/R1) + (1/R2) + (1/R3) |
| RC circuits time constant: | τ = RC |
| Magnetostatics | |
| Magnetic force on a moving charge: | F = qv × B |
| Magnetic force on a long straight wire: | F = IL × B |
| Charged particle in a magnetic field: | r = mv/(qB) |
| The magnetic field of a long straight wire: | B = μ0I/(2πr) |
| The magnetic field inside a solenoid: | B = μ0nI |
| Current loops | |
| Magnetic moment: | μ = IAn |
| Torque: | τ = μ × B, τ = μB sinθ |
| Potential energy: | Uμ = -μB cosθ |
| Faraday's Law | |
| Faraday's law: | Induced emf = -ΔΦB/∆t (through a fixed area) |
| Magnetic flux: | ΔΦB= B ΔA cosθ |
| Induced current: | I = emf/R |
| Transformer: | V2/N2 = V1/N1, V2 I2 ≤ V1 I1 |
| Electromagnetic Waves | |
| Sinusoidal waves: | E(x,t) = Emaxsin(kx - ωt + φ), Brad = Erad/c |
| Energy flux S, intensity I: | S = (1/μ0)E × B, I is proportional to Emax2 |
| Polarizers: | Itransmitted = I0cos2θ. |
| Constants | |
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Elementary charge qe: Electron mass me: Proton mass mp:
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qe = 1.6 * 10-19 C me = 9.1 * 10-31 kg mp = 1.672 * 10-27 kg ke = 9*109 Nm2/C2 ε0 = 8.85*10-12 C2/(Nm2) μ0 = 4π*10-7 N/A2 |