Understanding and Solving Electrostatics Problems: Tips and Techniques

[Murgs2012]

Homework Statement

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

Homework 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)

The Attempt at a Solution

no idea how to approach it.

 

[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?

 

[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?

 

[rude man]

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

 

[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

 

[rude man]

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

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.