Electrostatics

F = ma

F = kq₁q₂/r²

k = 1/4pe₀

E = F/q_o

E = kq/r² (point charge)

W_AB = EPE_A – EPE_B

V = EPE/q_o

V_B – V_A = -W_AB/q_o

V = kq/r (point charge)

q = CV

Energy = ½ qV = ½ CV² = q²/2C

Energy density =1/2Î_oE²

Circuits

C_P = C₁ + C₂ + ...

1/C_s = 1/C₁ + 1/C₂ + ...

I = Dq/Dt

V = IR (Resistor)

R = rL/A (Resistance)

P = IV (Power)

R_S = R₁ + R₂ + ...

1/R_P = 1/R₁ + 1/R₂ + ...

q = q_o[1-e^-t/RC] (Charging)

q = q_oe^-t/RC (Discharging)

Magnetism

F = q_ovBsinq (force on moving charge)

F = ILBsinq (force on wire)

t = NIAB sinf (torque on loop)

B = m_oI/2pr (wire)

B = Nm_oI/2R (loop)

B = m_onI (solenoid)

F = BA cosf (flux)

E = -NDF/Dt (Induced emf)

w = 2pf

Energy = ½ LI² (Inductor)

Energy density = 1/(2m_o) B²

r = mv/qB (radius of particle in Bfield)

AC Circuits

V_s/V_p = Ns/Np (Transformer)

I_rms = I_MAX/Ö2

V_rms =V_MAX/Ö2

X_C = 1/(2pfC) (Reactance)

X_L = 2pfL (Reactance)

V = IZ (Generator)

V = I X_L (Inductor)

V = I X_C (Capacitor)

Z = (R² + (X_L - X_C)²)^1/2

f_o = 1/(2pÖLC) (Resonance)

P = I²_rms R (Power)

Phase angle

tan f = (X_L - X_C)/R = (V_L - V_C)/V_R

cos f = V_R/V_o

sin f = (V_L - V_C)/V_o

E&M Waves

c = fl (Wave equation)

I = I_o cos²q (Polarization)

f’ = f(1⁺/- v/c) (Doppler effect)

Miror
Parallel – Focal Point
Focal Point – Parallel
Center of curvature-center of curvature

Lens

Parallel – Focal Point
Focal Point – Parallel

Straight through the middle

Lenses and Mirrors

1/f = 1/d_o + 1/d_i

m = h_i/h_o = -d_i/d_o

n₁sinq₁ = n₂sinq₂ (Snell’s Law)

sin q_c = n₂/n₁ (Critical angle)

tan q_b = n₂/n₁ (Brewster’s angle)

Interference

l₂-l₁= (m+1/2)l_film (Destructive)

l₂-l₁= m l_film (Constructive)

Double Slit

sin q = ml/d (Bright)

sin q = (m+1/2)l/d (Dark)

Thin Film

l₂-l₁ = 2t

l_film = l_vac/n_film

n₁ < n₂ (1/2 l phase shift)

Single slit/Diffraction

sinq = m l/W (Dark) (single)

sinq = m l/d (Bright) (diff)

Photons

E = hf

hf = KE_max + W_o (Photoelectric Effect)

l’- l = h/mc (1-cos q) (Compton)

l = h/p (De Broglie)

(Dp_y)(Dy) > h/4p (Heisenberg)

Constants

k = 8.99x10⁹ Nm²/C²

e₀ = 8.85x10^-12 C²/Nm²

e = 1.60x10^-19 C

m_o = 4p x10^-7 Tm/A

c = 3x10⁸ m/s

h = 6.62 x10^-34 J*s

m_e = 9.109 x10^-31 kg