January 23, 2009
PHY 712 - Problem Set #3

Continue reading Chaper 1 & 2 in Jackson; homework is due Monday, Jan. 26, 2009.

  1. Consider a one-dimensional charge distribution of the form:

    \begin{displaymath} \rho(x) = \left\{ \begin{array}{lll} 0 \;\; & {\rm {for}}\... ...0 \;\;\; & {\rm {for}} \; & x \geq a/2, \end{array} \right. \end{displaymath}

    where $\rho_0$ and $a$ are constants.
    1. Solve the Poisson equation for the electrostatic potential $\Phi(x)$ with the boundary conditions $\Phi(-a/2) = 0$ and $\frac{d \Phi}{dx}(-a/2) = 0$.
    2. Find the corresponding electrostatic field $E(x)$.
    3. Plot $\Phi(x)$ and $E(x)$.
    4. Discuss your results in terms of elementary Gauss's Law arguments.

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