Decaying E-Field: Spatially Uniform in Conductors

[sachi]

We are asked to show that we can have a "spatially uniform E-field" in a conductor according to E=Eo*exp(-t/tau) where tau=ErEo/sigma

where Er is the relative permittivity and sigma is the conductivity. I know we need to use curl(H) = ErEo*dE/dt + sigma*E
and for some reason we say that curl H is equal to zero. then we get a simple ODE to solve. I'm having trouble coming up with a geometrical argument for why curl(H) = zero. any hints appreciated.

 

[Physics Monkey]

If the electric field is spatially uniform, what does the $$\nabla \times E = - \frac{\partial B}{\partial t}$$ equation imply about $$B$$ and $$H$$?

 

[sachi]

I'm not too sure about the meaning of "spatially uniform". If we just assume that E=E(t) and let it be in say the x direction then we can show that curl(E) has no x components, and the rest of the problem works out. But surely a wave has to have some spatial dependence e.g E = E(z,t)?

 

[Physics Monkey]

Nope, spatially uniform means independent of position. Indeed, as you show here, spatially uniform solutions do exist though of course they are ultimately unphysical.