- #1
pcflores
- 9
- 0
Homework Statement
given a medium in which p=0, j=0 but where the polarization vector P=P(r,t). Derive the wave equation satisfied by E and B.
Homework Equations
i started with the 4 basic Maxwells equations
∇ · D = ρ (1)
∇ · B = 0 (2)
∇ × E = −∂B/∂t (3)
∇ × H = J + ∂D/∂t (4)
and with the relation
D = ɛE + P (5)
H = 1/µB + M (6)
The Attempt at a Solution
i took the curl of both sides of 3 and simplified both sides and got the eqaution
laplacian of E = µ∂H/∂t (7)
i assumed that M=0 --> B=µH
taking the curl of both sides of (7) and using (4)
curl of (laplacian of E) = (µ∂/∂t)∂(∇ × D)/∂t (8)
substituting (5) to (8)
laplacian of E = (µɛ∂/∂t)∂E/∂t + µ∂/∂t)∂P/∂t (9)
my final answer is for the wave equation of E is (9), i want to know if my answer is correct before trying to solve Bthank you in advance