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Homework Help: Charges and field

  1. Feb 1, 2010 #1
    A line charge of uniform charge density lambda forms a circle of radius b that lies in the x-y plane with its centre at the origin.
    a)Find the electric field E at the point (0,0,h).
    b)At what value of h will E in parta) be a maximum?What is this maximum?

    ans:
    a)E=人hb/(2e0(h^2+b^2)^1/2 >k(direction of K)
    b)h=b/2^1/2 ; Emax=人/(3^3/2*e0*b)
     
  2. jcsd
  3. Feb 1, 2010 #2
    If you have the answers, what is the problem?
     
  4. Feb 3, 2010 #3
    the method how to do it
     
  5. Feb 3, 2010 #4
    I think using the equation for an electric field due to a line charge is a good place to start:

    [tex]
    \mathbf{E}(\mathbf{r})=\frac{1}{4\pi\varepsilon_0}\int_\mathcal{P}\frac{\lambda(\mathbf{r}')}{\mathcal{R}^2}\hat{\mathbf{\mathcal{R}}}dl'
    [/tex]

    Fortunately for you, the line charge is of a uniform density, so this can be reduced to

    [tex]
    \mathbf{E}(\mathbf{r})=\frac{\lambda}{4\pi\varepsilon_0}\int_\mathcal{P}\frac{1}{\mathcal{R}^2}\hat{\mathbf{\mathcal{R}}}dl'
    [/tex]

    What can you tell me about [itex]\mathcal{R}[/itex]--the separation length--and [itex]\hat{\mathbf{\mathcal{R}}}[/itex]--the separation vector?
     
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