It's a classic problem that you'll find near the beginning of just about any college textbook on electromagnetism: a positive charge is placed above a large, conducting sheet of metal, and the question is to determine the resulting electric field.

It's a hard problem, in principle: the positive charge is going to attract a whole bunch of negative charges to accumulate beneath it on the surface of the sheet, and those induced charges create their own contribution to the field. The catch is that we don't know in advance how those charges are going to distribute themselves! So how can we possibly compute the electric field if we don't even know where all the charges are?

The original solution to the puzzle dates back to William Thomson—aka Lord Kelvin—in the mid-1800s, using a trick he invented called the method of images. And that trick is still how you'll typically find this problem solved in textbooks to this day. Proving why it actually works, though, requires quite a bit of fairly advanced math about boundary value problems and uniqueness theorems.

But there's a simpler approach—one based on symmetry—that requires essentially nothing more than a high-school-level understanding of Coulomb's law. And that's what I'll explain in this video. Along the way, we'll learn about some of the fundamental properties of conductors, and we'll get a peek at where Kelvin's method of images comes from in the first place.

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