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Suppose we have a fixed point charge in front of a half cylinder. Can we find energy of system using this method? If so, how?

I have seen image method being used for infinite sheets. Can we use it if we had say a sector of sphere.

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  • $\begingroup$ Not clear. What do you mean by a spherical section combined with ray optics? Are you asking if the method of images can be used for a point charge near a spherical conductor? Aren't you asking about a cylinder? $\endgroup$ – sammy gerbil Jun 18 '18 at 20:39
  • $\begingroup$ about both sphere and cylinder or other curves $\endgroup$ – 3.14159 Jun 19 '18 at 14:13
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In electrostatics, there are some well-known image method problems such as a point charge with an infinite sheet boundary, a point charge with a spherical boundary, or an infinite line charge with a parallel infinite cylinder.

Especially in two dimensions, the generalization to arbitrary curved boundaries is possible. It is called the "Schwarzian reflection" and involves complex analysis. A good reference is

Needham, T. (1998). Visual complex analysis. Oxford University Press. pp. 532-538 and pp.252-257.

However, it seems that the problem you stated, a point charge in front of a cylinder, is hard to attack with the method of images. Green's function in a given boundary can be regarded as a generalization of the notion of image charges, so in principle, we can find the image charges for the problem; but I'm afraid that it might be not so easy to find the image charges not involving specific mathematical calculations.

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