Formulas 3

Faraday's Law

 
  • Faraday's law:
Induced emf = ∫around loopE·dr = -∂ΦB/∂t (through a fixed area)
  • Magnetic flux:
 ΦB = ∫AB·dA,  dΦB = B dA cosθ, 
  • Induced current:
I = emf/R
  • Transformer:
V2/N2 = V1/N1,    V2 I2  ≤  V1 I1

Electromagnetic Waves

 
  • Energy density in EM fields:
u = ½ε0E2 + B2/(2μ0)
  • Energy flux S, intensity I:
S = (1/μ0)E × B,  I is proportional to Emax2
  • Sinusoidal waves:
E(x,t) = Emaxsin(kx - ωt + φ),  Brad = Erad/c
  • Polarizers:
Itransmitted = I0cos2θ.

Geometrical Optics

 
  • Law of reflection:
θ1 = θ2
  • Law of refraction:
n1sinθ1 = n2sinθ2
  • Total internal reflection:
sinθc = n2/n1
  • Mirror equation:
1/xo + 1/xi = 1/f,  M = -xi/xof = R/2
  • Lens equation:
1/xo + 1/xi = 1/f,  M =- xi/xo

Wave Optics

 
  • Double slit, diffraction grating (maxima):
d sinθ = mλ, m = 0, 1, 2, ...
  • Single slit (minima):
w sinθ = mλ, m = 1, 2, ...
  • Resolving power:
θmin = 1.22 λ/D
  • Constructive interference (thin oil film on water):
2noiltcosθt = (m+1/2)λ, m = 0,1,2,…