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Electromagnetism Help required

  1. Dec 31, 2014 #1
    [Mentor's note: this thread was originally posted in a non-homework forum, therefore it does not have the homework template.]

    ------------

    I have a question which is:


    Let [itex]\vec{E} = E_0 \cdot (-y,x, z) [/itex] Can [itex]\vec{E}[/itex] 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 [itex]\vec{E} = E_0 \cdot \vec{r} ) [/itex] Can [itex]\vec{E}[/itex] 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.
     
    Last edited by a moderator: Jan 1, 2015
  2. jcsd
  3. Dec 31, 2014 #2

    ShayanJ

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    Gold Member

    An electrostatic field, is an electric field for which we can find an scalar field(a function of spatial coordinates)[itex] \phi [/itex] such that [itex] \vec E=-\vec \nabla \phi [/itex]. Now if I take the curl of this equation, I get [itex] \vec \nabla \times \vec E=0 [/itex](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.
     
  4. Dec 31, 2014 #3
    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?
     
  5. Dec 31, 2014 #4

    ShayanJ

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    Gold Member

    [itex]
    \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
    [/itex]
    And [itex] E_0 [/itex] is only a constant.
     
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