Answer to Question #292158 in Physics for Shah

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.