Electromagnetism Help required

[henrybrent]

[Mentor's note: this thread was originally posted in a non-homework forum, therefore it does not have the homework template.]

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I have a question which is:


Let $\vec{E} = E_0 \cdot (-y,x, z)$ Can $\vec{E}$ be an electrostatic field? if yes, find the charge density which generates this field. If not, find the magnetic field which generates it


and,

Let $\vec{E} = E_0 \cdot \vec{r} )$ Can $\vec{E}$ be an electrostatic field? if yes, find the charge density which generates this field. If not, find the magnetic field which generates it


I have no idea where to start, any help is appreciated.

 

[ShayanJ]

An electrostatic field, is an electric field for which we can find an scalar field(a function of spatial coordinates)$\phi$ such that $\vec E=-\vec \nabla \phi$. Now if I take the curl of this equation, I get $\vec \nabla \times \vec E=0$(because the curl of the gradient of a scalar field is always zero). So you should see whether the curl of the given electric fields are zero or not.

 

[henrybrent]

I am not sure how to take curl of the electric fields, sorry.

I am not sure what E_0 denotes? is that merely a constant?

 

[ShayanJ]

$\vec \nabla \times \vec E=\vec \nabla \times (E_x,E_y,E_z)=(\frac{\partial E_z}{\partial x}-\frac{\partial E_y}{\partial z})\hat x+(\frac{\partial E_x}{\partial z}-\frac{\partial E_z}{\partial x})\hat y+(\frac{\partial E_y}{\partial x}-\frac{\partial E_x}{\partial y})\hat z$
And $E_0$ is only a constant.