Question

Solve Laplace's Equation nabla^2 V(z)=0.

Answer 1

To solve Laplace's equation

$$\nabla^2 V(z)=0,$$

we need to know how the function $V(z)$ looks. However, the solution can be written as

$$\nabla^2V(z)=\dfrac{\partial^2 V(z)}{\partial z^2}=0,\\\space\\ V(z)=mz+c,$$

where m and c are constants defined by boundary conditions.