How do you differentiate Poisson's equation?

Answer 1

To differentiate Poisson's equation, which is given by (\nabla^2 \phi = -\frac{\rho}{\epsilon_0}), you apply the Laplacian operator (\nabla^2) to the potential function (\phi). This involves taking the second partial derivatives of (\phi) with respect to spatial variables. If you need to differentiate it with respect to time or other variables, you would need to consider the context of the problem, as Poisson's equation typically deals with static fields. Note that Poisson's equation itself is primarily a spatial differential equation.