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Heirot
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Homework Statement
Let's say we have a wire of finite length L with total charge Q evenly spread along the wire so that lambda=Q/L, linear charge density, is constant. The wire is shaped in x-y plane in some well behaved curve y = f(x). Find the surface charge density sigma(x,y).
Homework Equations
Q = Int(lambda dl) = Int ( Sqrt(1+(dy/dx)^2) dx) for line charge density
Q = Int(sigma(x,y) dx dy) for surface charge density
The Attempt at a Solution
The most logic thing to do would be to write sigma(x,y) = lambda * delta(y-f(x)), where delta(x) is Dirac's delta function. Unfortunately, this doesn't give the right Q, because integration of the delta function over y only give 1 and not the required Sqrt(1+(dy/dx)^2).
Where's the error in reasoning?