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 \(\sigma=\sigma_{0} \cos \varphi,\) where \(\varphi\) is the polar angle of the cylindrical coordinate system whose \(z\) axis coincides with the axis of the given surface. Find the magnitude and direction of the electric field strength vector on the \(z\) 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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