In: Physics
U(x, y) = ½ [φ(x+iy) + φ(x-iy)] and V(x, y) = i/2 [φ(x+iy) –φ(x-iy)]
A) For φ(z) = z2 find U and V and their induced vector fields E =▼U and
F =▼V also show that ▼2U = ▼2V = 0
B) Repeat for f(z) = z3
C) For f(z) = ln z we get U(x, y) = ½ ln (x2+y2) and V(x, y) = arctan (y/x) Find ▼U (electrostatic field) and ▼V (magnetic field) . Also, show that ▼2U = ▼2V = 0 for x2+y2 ǂ 0.