Consider a sphere of radius R, carrying a charge density p(r) = ar. The total charge of the sphere is a known value Q. (a) Calculate the constant a and the electric field (maanitude and direction) inside and outside the sphere, as a function of Q and R. (b) Calculate the potential in the origin, as a function of Q and R. (c) Suppose now that the charge Q is uniformly distributed on the surface of the same sphere. Calculate the difference of electrostatic energy between the final and initial configurations.
Consider a sphere of radius R, carrying a charge density p(r) = ar. The total charge of the sphere is a known value Q. (a) Calculate the constant a and the electric field (maanitude and direction) inside and outside the sphere, as a function of Q and R. (b) Calculate the potential in the origin, as a function of Q and R. (c) Suppose now that the charge Q is uniformly distributed on the surface of the same sphere. Calculate the difference of electrostatic energy between the final and initial configurations.
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Transcribed Image Text:Consider a sphere of radius R, carrying a charge density p(r) = ar. The total charge of
the sphere is a known value Q.
(a) Calculate the constant a and the electric field (maanitude and direction) inside
and outside the sphere, as a function of Q and R.
(b) Calculate the potential in the origin, as a function of Q and R.
(c) Suppose now that the charge Q is uniformly distributed on the surface of the
same sphere. Calculate the difference of electrostatic energy between the final
and initial configurations.
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