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a) Find the Green's function for Poisson's equation for the exterior of a sphere of radius a and use it to solve Poisson's equation V = -4πp(r) in the region outside the sphere, i.e. r > a, with the boundary condition (r = a, 0, 0) = F(0,0), where F(0, 0) is a given function. b) Assume the sphere consists of two metal hemisphered separated by a thin layer of insulator and that the two hemispheres are maintained at potentials +V and -V by a battery inside the sphere. Take p = 0 outside the sphere. Use the formula of part a) to find the potential along the axis above the middle of the hemisphere at potential +V.

a) Find the Green's function for Poisson's equation for the exterior of a sphere of radius a and use it to solve Poisson's equation V = -4πp(r) in the region outside the sphere, i.e. r > a, with the boundary condition (r = a, 0, 0) = F(0,0), where F(0, 0) is a given function. b) Assume the sphere consists of two metal hemisphered separated by a thin layer of insulator and that the two hemispheres are maintained at potentials +V and -V by a battery inside the sphere. Take p = 0 outside the sphere. Use the formula of part a) to find the potential along the axis above the middle of the hemisphere at potential +V.

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5. a) Find the Green's function for Poisson's equation for the exterior of a sphere of radius a and use it to solve Poisson's equation V₁ = −4лp(r) in the region outside the sphere, i.e. r > a, with the boundary condition (r = a, 0, 0) = F(0, 0), where F(0, 0) is a given function. b) Assume the sphere consists of two metal hemisphered separated by a thin layer of insulator and that the two hemispheres are maintained at potentials +V and -V by a battery inside the sphere. Take p = 0 outside the sphere. Use the formula of part a) to find the potential along the axis above the middle of the hemisphere at potential +V.
Transcribed Image Text:5. a) Find the Green's function for Poisson's equation for the exterior of a sphere of radius a and use it to solve Poisson's equation V₁ = −4лp(r) in the region outside the sphere, i.e. r > a, with the boundary condition (r = a, 0, 0) = F(0, 0), where F(0, 0) is a given function. b) Assume the sphere consists of two metal hemisphered separated by a thin layer of insulator and that the two hemispheres are maintained at potentials +V and -V by a battery inside the sphere. Take p = 0 outside the sphere. Use the formula of part a) to find the potential along the axis above the middle of the hemisphere at potential +V.
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