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In free space, the Poisson equation becomes the Laplace equation, which is given as (nabla^2 Phi = 0), where (Phi) represents the scalar potential field, and (nabla^2) is the Laplacian operator. This simplification occurs because in free space (a vacuum), there are no free charges, so the charge density (rho) is zero, which simplifies the Poisson equation (nabla^2 Phi = -frac{rho}{epsilon_0}) to the Laplace equation.
c
Explanation: The Poisson equation is given by Del
2
(V) = -ρ/ε. In free space, the charges
will be zero. Thus the equation becomes, Del
2
(V) = 0, which is the Laplace equation
c
Explanation: The Poisson equation is given by Del2 (V) = -ρ/ε. In free space, the charges will be zero. Thus the equation becomes, Del2(V) = 0, which is the Laplace equation.