Question

state and prove two dimensional Laplace equation in cartesian form

Answer 1

Laplace equation in Cartesian coordinates

• The Laplace equation is written

∇2φ = 0

• For example, let us work in two dimensions so we have to find

φ(x, y) from,

d² Φ /dx²+ d² Φ / dy²=0

• We use the method of separation of variables and write

φ(x, y) = X(x)Y (y)

• We use the method of separation of variables and write

φ(x, y) = X(x)Y (y)

X"/X'+Y"/Y'=0