All Problems Constant Electric Field in a Vacuum
Problem 3.13
A thin straight rod of length \(2 a\) carrying a uniformly distributed charge \(q\) is located in vacuum. Find the magnitude of the electric field strength as a function of the distance \(r\) from the rod's centre along the straight line (a) perpendicular to the rod and passing through its centre; (b) coinciding with the rod's direction (at the points lying outside the rod). Investigate the obtained expressions at \(r \gg a\).
3.13. (a) \(E=\frac{q}{4 \pi \varepsilon_{0} r \sqrt{a^{2}+r^{2}}}\) (b) \(E=\frac{q}{4 \pi \varepsilon_{0}\left(r^{2}-a^{2}\right)} .\) In both cases \(E \approx \frac{q}{4 \pi \varepsilon_{0} r^{2}}\) for \(r \gg a\)