- #1

- 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**= ɛ

**E**+

**P**(5)

**H**= 1/µ

**B**+

**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 B

thank you in advance