Electrostatics Question

1. Jan 6, 2014

Murgs2012

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

Any ideas on the way to approach them problems would be appreciated really.

2. Relevant equations

Assuming it has something to do with ∇.E=ρ/ε or ∫E.ds=Q/ε to see if the divergence of the E fields given satisfy them conditions, if not use ∇xE=-dB/dt or ∫E.dl=-d/dt∫(Bds)

3. The attempt at a solution
no idea how to approach it.

2. Jan 6, 2014

tikker

You are on the right way track with
$\vec{\nabla}\times\vec{E} =-\frac{\partial\vec{B}}{\partial t}$
For an electrostatic configuration there are no moving charges and hence no magnetic field. Knowing this, what will this equation become then?

3. Jan 6, 2014

Murgs2012

So for that equation in an electrostatic field ∇xE=0, and that would be the way to determine if it's electrostatic or not?
If it's electrostatic would you then use Gauss' law ∇.E=ρ/ε to find the charge density that creates this field.

If it's not electrostatic would the non zero result found for ∇xE= -dB/dt, so integrate with respect to time to determine the magnetic field that causes the electric field?

4. Jan 6, 2014

rude man

How about del dot D = rho?
(D = epsilon E).

5. Jan 6, 2014

Murgs2012

That's how we'd find the charge density Rho isn't it? But that's only part of the question, it was how to know if it was an electrostatic field that was annoying me

6. Jan 6, 2014

rude man

OK, I guess I assumed E0 was a constant. Then E is not a function of time and so must be electrostatic if it obeys the Poisson equation. Same for part c.

If E0 can be time-varying then it's more complicated.

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