Week 8 Dielectrics & Magnetisation Flashcards
what is the free charge density electric displacement equation
∇ * D = ρfree
what is the capacitance susceptibility equation
C = (1 + χ)C0
C0 is the capacitance in vacuum
what is the relative permeability susceptibility equation
εr = 1 + χ
what is the electric permeability displacement equation
D = εrε0E
what is the energy of a capacitor in terms of electric displacement
U = 1/2 ∫D*E dV
what are the two dielectric boundary statements
perpendicular electric displacement is constant across a boundary
parallel electric field is constant across a boundary
what are the parallel electric field and the perpendicular electric displacement equations
E1sinθ1 = E2sinθ2 D1cosθ1 = D2cosθ2
what is the relative permeability boundary equation
εr1cotθ1 = εr2cotθ2
what is the relative magnetic permeability equation
μr = L / Lvac
L is the inductance
what is the Magnetisation equation
M = nm
n is the number density
m is the average magnetic dipole moment
what is the magnetic moment equation
m = I A n^
what are the external energy and torque equations due to magnetic moment equations
Uext = -m * Bext τext = m x Bext
what is the linear isotropic magnetisation equation
M = χ/μ0 B
where χ is the magnetic susceptibility
what are the two magnetic susceptibility scenarios
χ < 0 corresponds to diamagnetism (induced)
χ > 0 corresponds to paramagnetism (align)
what is the diamagnetism magnetisation equation
M = ( -ne^2Z / 6m ) B
Z is the number of electrons
