Midterm 1 Flashcards
Faraday’s Law
Induced emf in any closed circuit is equal to the rate of change of the magnetic flux over time. This induced emf creates a current, which opposes the flux causing it (Lenz’s effect)
Ampere’s Law
Ampère’s circuit law states that the line integral of H around a closed path is the
same as the net current Ienc enclosed by the path
Stoke’s Law
Stokes’s theorem states that the circulation of a vector field A around a (closed) path
L is equal to the surface integral of the curl of A over the open surface S bounded
by L
(see Figure 3.21), provided A and A are continuous on S.
Gauss’s Law (general)
Gauss’s Law (magnetism)
An isolated magnetic charge does not exist
Lenz’s Law
Induced emf creates a current whose related magnetic flux will oppose the change in direction of the magnetic flux inducing the emf (conservation of energy)
Get from H to B
B=uH
What is H?
Magnetic field strength
Units: A/m (Amperes per metre)
What is B?
Magnetic flux density (B for Bensity)
Units: Tesla
What is D?
Electric flux density
D=ϵE
Units: C/m^2
What is ϵ?
Permittivity
Units: H/m (Henries per metre)
What is µ?
Permeability
Unit: F/m (henries per metre)
What is eta? (curly n)
Impedance of the medium
Units: Ohms
What is n?
Refractive index
n = sqrt(µrϵr)
What is beta?
Wave number or the propagation constant
beta=2*pi/λ
λ
Wavelength
Inverse of fs, spatial frequency
-sin(wt)=
cos(wt+pi/2)
Steps to derive the wave equation (in terms of Ex)
- Start with curl of E = -dB/dt
- B=uH
- cross of E =duHy/dt
- y component of cross of E = -udH/dt
- dEx/dz=-udHy/dt
- Then switch to cross of H = J + dD/dt
- J = 0
same process as before to get
x component of cross of H = edE/dt
Perfect dielectric
σ (conductivity) = 0
εr″/εr′= 0 (aka εr″=0) (permittivity)
ε (permittivity) is real
k=β
Lossy dielectric
σ (conductivity) = 0
ε (permittivity) is complex
Conductor
σ (conductivity) != 0
ε (permittivity) is real
Non-magnetic material
μ=μ0 (permeability)
k
w/v
k²
k²=-jwμ(σ+jwε)
