5. The Poisson equation8²+ax² ay² az²relates the electrostatic potential (r) = (x, y, z) to the charge distribution p(r) in vacuum. In partic-ular, when we are dealing with a point charge, we write this equation as7²4 = |8²əx²+8²8²əz²2²+ o(r)+ G5, 8) = - = 10²G(r, r')p(r)€0-83) (r-r'),where r' = (x, y, z) is the position of the point charge, 63) (r - r') = 6(x − x')8(y - y')6(z - z') is theDirac delta function in three-dimensional space. Solve for G(r, r') by performing a three-dimensionalFourier transform on the Poisson equation, followed by a three-dimensional inverse Fourier transform.You may use the result00 sinid=

Poisson's equation: ∇2ϕ=∂2∂x2+∂2∂y2+∂2∂z2ϕr→=-ρr→∈0 For a point charge:…

5. The Poisson equation 8² 8² + ø(r) = - əy² əz² relates the electrostatic potential (r) = (x, y, z) to the charge distribution p(r) in vacuum. In partic- ular, when we are dealing with a point charge, we write this equation as 7²6 = 10²2 [əx² + 8² 8² 8² əz² + + 8x² p(r) G(r. r) = --—-8¹ (r-r), -1/-0 where r' = (x, y, z) is the position of the point charge, 63) (r - r') = 8(x − x')6(y-y')(z-z') is the Dirac delta function in three-dimensional space. Solve for G(r, r') by performing a three-dimensional Fourier transform on the Poisson equation, followed by a three-dimensional inverse Fourier transform. You may use the result fd = sin

5. The Poisson equation 8² 8² + ø(r) = - əy² əz² relates the electrostatic potential (r) = (x, y, z) to the charge distribution p(r) in vacuum. In partic- ular, when we are dealing with a point charge, we write this equation as 7²6 = 10²2 [əx² + 8² 8² 8² əz² + + 8x² p(r) G(r. r) = --—-8¹ (r-r), -1/-0 where r' = (x, y, z) is the position of the point charge, 63) (r - r') = 8(x − x')6(y-y')(z-z') is the Dirac delta function in three-dimensional space. Solve for G(r, r') by performing a three-dimensional Fourier transform on the Poisson equation, followed by a three-dimensional inverse Fourier transform. You may use the result fd = sin