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Airsteve0

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## Homework Statement

The transformation z=1/2(w + 1/w) maps the unit circle in the w-plane into the line −1≤x≤1 in the z-plane.

(a) Construct a complex potential in the w-plane which corresponds to a charged

metallic cylinder of unit radius having a potential Vo on its surface.

(b) Use the mapping to determine the complex potential in the z-plane. Show that

the physical potential takes the value Vo on the line −1≤x≤1. This line thus

represents a metallic strip in the x-y plane.

## Homework Equations

F(w) = Φ(u,v)+iΨ(u,v) = (−λ/2πϵo)Ln(w) + Vo

x = 1/2(u + u/(u^2+v^2))

y = 1/2(v - v/(u^2+v^2))

## The Attempt at a Solution

So far I have worked out the relation between (x,y) and (u,v) as well as made an attempt at part (a) (answer show above). However, it is part (b) and using the mapping that I am completely lost with. Mainly, if I try to find u and v in terms of solely x and y I get 2 solutions (i.e. plus or minus because of squaring); this leaves me unsure of what to do. Any help would be wonderful!