Homework 2

Due: April 18, 2014 in class

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9. An infinite, grounded, conducting cylinder (radius a = 1) is placed in an electric field uniform at infinity. Assume that the axis of the cylinder lies along the z-axis and that the electric field at infinity is |E| = E_o in the y direction. The boundary conditions are that the electric potential V = 0 for r = a (the surface of the conducting cylinder) and V = - E_oy at infinity. Using the map

F(z) = z + 1/z

find the electrostic potential V everywhere. Here, z is not the coordinate but, rather, is z = x + iy. Sketch the equipotential surfaces and field lines.

10. Chapter 14, 11-5

that the electric potential V = 0 for r = a (the surface of the conducting cylinder) and V = - E_oy at infinity. Using the map
F(z) = z + 1/z
find the electrostic potential V everywhere. Here, z is not the coordinate but, rather, is z = x + iy. Sketch the equipotential surfaces and field lines.

11. Chapter 14, 11-11

Find the Laurent series of f(z) = e^z/(1-z) for |z| < 1 and |z| > 1.

12. Chaper 14, 11-35

Find expressions for the Cauchy-Riemann conditions in a general orthogonal curvilinear coordinte system.

13. Chapter 14, 2-24

Find out whether (y-ix)/(x²+ y²) is analytic.

14. Chapter 14, 3-20

15. Chapter 14, 4-4

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Solutions: Part 1 and Part 2