Consider a spherical volume charge distribution given by p(r) = po + ar 0 R where, r is the distance from the center of the sphere and po and a are constants. (a) Calculate the total charge contained inside the sphere of radius R. (b) Use Gauss' law to obtain the electric field everywhere due to the charge distri- bution. (c) Obtain V.Ē within and outside the sphere of radius R. (d) Obtain ▼ × Ē within and outside the sphere.
Consider a spherical volume charge distribution given by p(r) = po + ar 0 R where, r is the distance from the center of the sphere and po and a are constants. (a) Calculate the total charge contained inside the sphere of radius R. (b) Use Gauss' law to obtain the electric field everywhere due to the charge distri- bution. (c) Obtain V.Ē within and outside the sphere of radius R. (d) Obtain ▼ × Ē within and outside the sphere.
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Transcribed Image Text:Consider a spherical volume charge distribution given by
p(r) = Po + ar
0 <r < R
r > R
= 0
where, r is the distance from the center of the sphere and po and a are constants.
(a) Calculate the total charge contained inside the sphere of radius R.
(b) Use Gauss' law to obtain the electric field everywhere due to the charge distri-
bution.
(c) Obtain V.Ē within and outside the sphere of radius R.
(d) Obtain V × Ē within and outside the sphere.
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