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Homework Help: Definition of electric field dE due to a small charge dQ

  1. Nov 20, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi...
    How can one be sure that
    [tex]
    d\textbf{E}=\frac{kdQ}{r^2}(\cos\theta \textbf{i} + \sin\theta \textbf{j})
    [/tex]
    Is true for a small charge dQ
    Is there some derivation for this?

    2. Relevant equations


    3. The attempt at a solution

    I have a problem for homework that uses this equation... I know how to solve the problem, but I feel like I should know how this equation works since I dont want to just mindlessly plug in information... Thanks.
     
  2. jcsd
  3. Nov 20, 2008 #2
    A small enough charge dQ can be considered a point charge. The equation is just a statement of Coulomb's law.

    [tex]
    d\textbf{E}=\frac{kdQ}{r^2}\hat{r}
    [/tex]

    The unit vector [tex]\hat{r}[/tex] in Cartesian coordinates gives you what you have.
     
  4. Nov 20, 2008 #3
    Ohh okay I get it now, thanks. I understand where the sin and cosine come from now
    :)
    Thanks so much!
     
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