1. Consider a conformal mapping given by . How are lines parallel to x and y axes map?

2. A semi-circular region is bounded by the x-axis and a circular arc of radius 1 about the centre. The x – axis is grounded while the circular arc is maintained at a constant potential . Consider a conformal transformation to convert the region into a planar region, solve the Laplace’s equation and obtain an expression for the potential in the semi-circular region.

3. Two semi-infinite conductors make right angles with each other. The horizontally placed conductor is grounded while the vertical one is at a potential , there being a thin insulation. Find an expression for the potential in the region between the two planes.