Discussion
An electric field applied along the length of a long circular cylinder produces a polarization P. The depolarization field produced in this configuration is :
Answer: D
The depolarization field is 0.
The depolarization field is produced by the bound surface charge \(\sigma = \vec{P}\cdot\hat{n}\) on the faces the polarization meets. In a long cylinder polarized along its axis, P is parallel to the curved surface, so \(\vec{P}\cdot\hat{n} = 0\) there; bound charge appears only on the two end faces, which are very far apart and very small compared with the length.
The depolarization factor along the axis of a long needle-like cylinder is therefore zero. The value \(-4\pi P/3\) (Gaussian units) is the depolarization field of a sphere, with factor 1/3, and \(2\pi P\) is the magnitude for a cylinder polarized across its axis, with factor 1/2. A thin slab polarized normal to its face would give \(-4\pi P\).
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