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1. Charged onion Consider a uniformly charged solid sphere with radius a carrying the charge Qf. The sphere is surrounded by a concentric metallic spherical shell with radius b which is con- nected to ground. The volume between the sphere and the shell is filled with a linear di-electric material with relative permittivity ɛr. Starting from Maxwell's equations on differential form, calculate the displacement а) and electric fields in the three regions:r b. Calculate the bound surface charge at r = a andr = b and relate it to the discon- b) tinuities in the electric field. [If you did not solve part a) you can use E,r

1. Charged onion Consider a uniformly charged solid sphere with radius a carrying the charge Qf. The sphere is surrounded by a concentric metallic spherical shell with radius b which is con- nected to ground. The volume between the sphere and the shell is filled with a linear di-electric material with relative permittivity ɛr. Starting from Maxwell's equations on differential form, calculate the displacement а) and electric fields in the three regions:r b. Calculate the bound surface charge at r = a andr = b and relate it to the discon- b) tinuities in the electric field. [If you did not solve part a) you can use E,r

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1. Charged onion Consider a uniformly charged solid sphere with radius a carrying the charge Qf. The sphere is surrounded by a concentric metallic spherical shell with radius b which is con- nected to ground. The volume between the sphere and the shell is filled with a linear di-electric material with relative permittivity ɛr. Starting from Maxwell's equations on differential form, calculate the displacement а) and electric fields in the three regions:r<a, a < r < b, r > b. Calculate the bound surface charge at r = a andr = b and relate it to the discon- b) tinuities in the electric field. [If you did not solve part a) you can use E,r<a = c1rî and Ea<r<b = C1a³/(r²e,) î.] c) Calculate the potential at the center of the solid sphere.
Transcribed Image Text:1. Charged onion Consider a uniformly charged solid sphere with radius a carrying the charge Qf. The sphere is surrounded by a concentric metallic spherical shell with radius b which is con- nected to ground. The volume between the sphere and the shell is filled with a linear di-electric material with relative permittivity ɛr. Starting from Maxwell's equations on differential form, calculate the displacement а) and electric fields in the three regions:r<a, a < r < b, r > b. Calculate the bound surface charge at r = a andr = b and relate it to the discon- b) tinuities in the electric field. [If you did not solve part a) you can use E,r<a = c1rî and Ea<r<b = C1a³/(r²e,) î.] c) Calculate the potential at the center of the solid sphere.
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