# Homework Help: Manipulation of Electromagnetic fields using curls clarification

1. Feb 11, 2014

### gedanken6

1. The problem statement, all variables and given/known data
Question 1. General Plane Waves.
We may represent a general electromagnetic plane wave by (real part of the complex exponentials)
$E=E_{0}*e^(i*k*r-iwt) B=B_{0}*e^(i*k*r-iwt)$

Show that Faraday's Law becomes iwB0=-ik x Eo
2. Relevant equations

dB/dt=- curl of E

3. The attempt at a solution
I transformed dB/dt into iwB0e^(ikr-iwt).

Attempted to perform curl of E on Eoe^(ikr-iwt) but not sure how to work with the r. I thought you might use curl in spherical polars but then you have theta and phi components and I think there's only x, y and z

2. Feb 11, 2014

### tiny-tim

hi gedanken6!
just because there's an r, that doesn't mean it stands for "radius"!

k*r simply means kxi + kyj + kzk

(erm … different k)

3. Feb 11, 2014

### vanhees71

No, it's the dot product:
$$\vec{k}\cdot \vec{r}=k_x x+k_y y+k_z z.$$

4. Feb 12, 2014

### tiny-tim

oops!

thanks, vanhees71!

5. Feb 12, 2014

### rude man

Start with faraday's law, use Stokes' theorem to produce Maxwell's law for del x E, then just use the given plane wave equations to show the validity of the given relationship between E0 and B0, which is just a matter of some differential calculus.