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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6420 • PDE

Fall 1998 • Question 7

Question

Math 6420 • PDE Fall 1998 • Question 7

Using conformal mapping find the electrostatic potential \(\phi (x,y)\) in the region between the circumferences \[ \gamma =\{z:\ |z|=1\}\qquad \text {and}\qquad \Gamma =\{z:\ |z-1|=2.5\} \] satisfying the boundary conditions \[ \phi \equiv 0\text { on }\gamma ,\qquad \phi \equiv 1\text { on }\Gamma . \]

Raw LaTeX

Using conformal mapping find the electrostatic potential
\(\phi(x,y)\) in the region between the circumferences
\[
  \gamma=\{z:\ |z|=1\}\qquad\text{and}\qquad \Gamma=\{z:\ |z-1|=2.5\}
\]
satisfying the boundary conditions
\[
  \phi\equiv 0\text{ on }\gamma,\qquad \phi\equiv 1\text{ on }\Gamma.
\]

Topic Tags

Boundary Value Problems Complex Potential Flow and Blasius Formula Conformal Mapping and Bilinear Transformations Linear Programming and Optimization