Finding charge density generating an Electric Field

[Ryomega]

Homework Statement

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

Homework Equations

∇ x E = 0 (following stoke theorem)

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

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

 

[joseirs]

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

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

 

[Ryomega]

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