Deriving wave eqn. from Faraday & A.M.

[Roodles01]

Homework Statement

I'm asked to start from Faradays Law & Ampere-Maxwell law then derive the equation for the magnetic field, B, in the form;

del²B = 1/c² * d²B/dt²

Homework Equations

Faraday: curl E = -dB/dt
A.M : curl B = ε₀μ₀ dE/dt

The Attempt at a Solution

taking curl of both sides of AM

rhs
curl curlB = grad div B - del²B
no monopole says divB = 0
so = - del²B

lhs
curl curl B = ε0μ0 curl dE/dt
rearrange
= ε0μ0 d/dt curl E
Faraday says curl E = -dB/dt

in the next step of working out I don't get why this goes to
-ε0μ0 d²B/dt²
instead of
-ε0μ0 dB/dt

Addled, I must be [Yoda]

 

[MisterX]

$-\nabla ^2 \mathbf{B} = \epsilon_0 \mu_0 \frac{\partial}{\partial t}\nabla \times E$

Try the substitution for $\nabla \times E$ again.

 

[Roodles01]

Thank you.
Nose - Face - well known phrase.