4. Maxwell's equations in matter

Question 1

What is the equation for surface charge density?

Answer 1

σ_P = P · n

Question 2

What is the equation for dipole moment?

Answer 2

P=qs

Question 3

What is the definition of polarisation?

Answer 3

The dipole moment per unit volume

Question 4

What is the equation for volume charge density?

Answer 4

ρ_P = −∇ · P

Question 5

What is the equation for polarisation current density?

Answer 5

J_P=∂/∂t P

Question 6

What is the equation for the total polarisation?

Answer 6

P=ε₀χE

Question 7

What is the equation for the polarisation field strength?

Answer 7

E_P=-P/ε₀

Question 8

What are the contributions to the total electric field?

Answer 8

E=E_app+E_P

Question 9

What is the relative permativity?

Answer 9

ε_r=1+χ

Question 10

What is the magnetic dipole moment?

Answer 10

m=IA
A is the area
I is the current

Question 11

What is the definition of magnetisation?

Answer 11

The magnetic dipole moment per unit volume

Question 12

What are the components of the magnetisation?

Answer 12

M_z=I∆x∆y etc

Question 13

What is the equation for magnetisation current density?

Answer 13

j_M=M × n
Where n is the outward facing normal

Question 14

What is the equation for the volume magnetisation current?

Answer 14

J_M=∇ × M

Question 15

What are the components of the total charge density?

Answer 15

ρ = ρ_f + ρ_P
f and P refer to the free and bound charges

Question 16

What is the equation for the displacement?

Answer 16

D=ε₀E+P=ε₀ε_rE

Question 17

What is Gauss’s law for matter?

Answer 17

∇ · D = ρ_f

Question 18

What is the equation for the magnetic field strength?

Answer 18

H=B/µ₀ − M
Where B is the magnetic flux density

Question 19

What is Ampere’s law for matter?

Answer 19

∇ × H = J_f +∂D/∂t

Question 20

What is the magnetic susceptibility?

Answer 20

M = χ_mH

Question 21

What is Maxwell’s first equation for matter?

Answer 21

∇ · D = ρ_f

Question 22

What is Maxwell’s second equation for matter?

Answer 22

∇ · B = 0

Question 22

What is Maxwell’s third equation for matter?

Answer 22

∇ × E = −∂B/∂t

Question 23

What is Maxwell’s fourth equation for matter?

Answer 23

∇ × H = J_f +∂D/∂t

Question 23

How do the parallel components of the electric field relate for a boundary?

Answer 23

E_2,||=E_1,|| The parallel component is continuous across the boundary

Question 23

How do the displacement and electric field relate?

Answer 23

D=ε₀E+P

Question 24

How do the magnetic flux density and magnetic field strength relate?

Answer 24

B = µ₀ (H + M)

Question 25

What is the equation for the change of displacement through a boundary?

Answer 25

D_1,⊥ − D_2,⊥ = σ_f

Question 26

What is the equation for the change of magnetic flux density through a boundary?

Answer 26

B_1,⊥ = B_2,⊥

Question 27

What are the equations for an EM wave through a boundary?

Answer 27

n × (E₂ − E₁) = 0, n · (D₂ − D₁) = σ_f , n · (B₁ − B₂) = 0, n × (H₂ − H₁) = j_f .