# Homework Help: Finding charge density generating an Electric Field

1. Jun 13, 2012

### Ryomega

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

Show that electrostatic field E = br
where b is a constant
is irrotational

Find the charge density ρ(r) which can generate this electric field

2. Relevant equations

∇ x E = 0 (following stoke theorem)

ρ = ε0(div E) since: div E = $\frac{ρ}{ε}$

3. The attempt at a solution

The first part (I'm assuming) will suffice as ∇ x E = 0

The second part ρ = ε0(div E) = ε0(div br) = bε0(div r)

The question is whether I can compute (div r) or not. Does "r" in this particular case equal to square root (x+y+z)2? I'm assuming I can't know data given, which is why I am tempted to leave the solution as it is.

Thanks

2. Jun 13, 2012

### joseirs

You cannot take the divergence of a scalar, so I suppose that r is actually the vector:

$\vec r=(x,y,z)$

3. Jun 13, 2012

### Ryomega

Ah good, that's what I was thinking. Thanks

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