A conducting cylindrical pipe of radius R and infinite length is sawn lengthways into two equal halves. A battery connected between the two establishes a potential on the upper half and –on the bottom half.
Write down the general form of the solution for cylindrical symmetry in terms of a sum over an infinite series of functions of polar coordinates ꚃ and e., Write
For appropriate
What condition on your solution gives a finite potential as
Find the coefficient for the field inside the cylinder by applying an orthogonality condition on your functions
Evaluate the potential as and check that it makes physical sense?
Evaluate the charge density living on the top half of the cylinder. Does it make sense?
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