All Problems

Constant Electric Field in a Vacuum

Problem 3.13

A thin straight rod of length 2a2 a carrying a uniformly distributed charge qq is located in vacuum. Find the magnitude of the electric field strength as a function of the distance rr 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≫ar \gg a.

Reveal Answer
3.13. (a) E=q4πε0ra2+r2E=\frac{q}{4 \pi \varepsilon_{0} r \sqrt{a^{2}+r^{2}}} (b) E=q4πε0(r2−a2).E=\frac{q}{4 \pi \varepsilon_{0}\left(r^{2}-a^{2}\right)} . In both cases E≈q4πε0r2E \approx \frac{q}{4 \pi \varepsilon_{0} r^{2}} for r≫ar \gg a
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