Question: Consider the conformal mapping w = 2a/2, where z=r+iy is a complex variable. (a) What kind of curves in the z-plane map to straight lines

Consider the conformal mapping w = 2a/2, where z=r+iy is a complex variable. (a) What kind of curves in the z-plane map to straight lines in the w-plane? (b) Use (a) to find the potential outside an infinitely long metal cylinder of radius R at electric potential V, separated by an insulating strip from a metal plate. Take the axis of the cylinder perpendicular to the c-y plane, the insulating strip along the direction of the cylinder, and the metal plate on the 1 - plane, where I, y and 2 are the three orthogonal axes of the Cartesian coordinates. Consider the conformal mapping w = 2a/2, where z=r+iy is a complex variable. (a) What kind of curves in the z-plane map to straight lines in the w-plane? (b) Use (a) to find the potential outside an infinitely long metal cylinder of radius R at electric potential V, separated by an insulating strip from a metal plate. Take the axis of the cylinder perpendicular to the c-y plane, the insulating strip along the direction of the cylinder, and the metal plate on the 1 - plane, where I, y and 2 are the three orthogonal axes of the Cartesian coordinates

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