All Problems

Constant Electric Field in a Vacuum

Problem 3.23

An infinitely long cylindrical surface of circular crosssection is uniformly charged lengthwise with the surface density σ=σ0cos⁡φ,\sigma=\sigma_{0} \cos \varphi, where φ\varphi is the polar angle of the cylindrical coordinate system whose zz axis coincides with the axis of the given surface. Find the magnitude and direction of the electric field strength vector on the zz axis.

Reveal Answer
E=1/2σ0/ε0, with the direction of the vector E corresponding to the angle φ=πE=1 / 2 \sigma_{0} / \varepsilon_{0}, \text { with the direction of the vector } \mathbf{E} \text { corresponding to the angle } \varphi=\pi
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