Static Fields: Fall-2025
HW 06: Due W3 D5

  1. Electric Field of a Point Charge from the Potential

    The electrostatic potential due to a point charge at the origin is given by: \begin{equation*} V=\frac{1}{4\pi\epsilon_0} \frac{q}{r} \end{equation*}

    1. Find the electric field due to a point charge at the origin as a gradient in rectangular coordinates.
    2. Find the electric field due to a point charge at the origin as a gradient in spherical coordinates.
    3. Find the electric field due to a point charge at the origin as a gradient in cylindrical coordinates.

  2. Electric Field of a Line Source From Potential

    Find the electric field around an infinite, uniformly charged, straight wire, starting from the following expression for the electrostatic potential: \begin{equation*} V(\vec r)=\frac{2\lambda}{4\pi\epsilon_0}\, \ln\left( \frac{ s_0}{s} \right) \end{equation*}

  3. Line Sources Using Coulomb's Law
    1. Find the electric field around a finite, uniformly charged, straight rod, at a point a distance \(s\) straight out from the midpoint, starting from Coulomb's Law.
    2. Find the electric field around an infinite, uniformly charged, straight rod, starting from the result for a finite rod.