# Electromagnetism Help required

• henrybrent
In summary, the conversation discusses whether the given electric fields can be classified as electrostatic fields, and if so, how to find the charge density that generates them. The conversation also explores taking the curl of the electric fields and the role of E_0 as a constant.

#### 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.

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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.

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?

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