# Homework Help: Deriving wave eqn. from Faraday & A.M.

1. Apr 22, 2013

### Roodles01

1. The problem statement, all variables and given/known data
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

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

3. 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
-ε0μ0 dB/dt

Addled, I must be [Yoda]

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Last edited: Apr 22, 2013
2. Apr 22, 2013

### MisterX

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

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

3. Apr 22, 2013

### Roodles01

Thank you.
Nose - Face - well known phrase.