B6. A solid, non-conducting sphere of radius R and relative permittivity e, = 4, is located at the origin. It carries aspherical but nonuniform volume charge density%3Dp(r) = Po\R'(3)with po constant.a)Show that the total charge in the sphere is Qo = 7PR³.b)Find the E-field at a point īpxâ outside the sphere (x > R).c)Find E at a point ī, = rŷ inside the sphered)Find the electric potential V just outside the sphere.e)Qo as before. Does the Ē-field at a point ī, = xâ change? Explain your reasoning carefully.Suppose we replace the non-conducting sphere by a conducting sphere of radius R carrying charge

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6. A solid, non-conducting sphere of radius R and relative permittivity e, = 4, is located at the origin. It carries a spherical but nonuniform volume charge density p(r) = PoV R' (3) with po constant. a) Show that the total charge in the sphere is Qo = T POR³. b) Find the E-field at a point , = xâ outside the sphere ( > R). c) Find E at a point r, = rŷ inside the sphere d) Find the electric potential V just outside the sphere.

6. A solid, non-conducting sphere of radius R and relative permittivity e, = 4, is located at the origin. It carries a spherical but nonuniform volume charge density p(r) = PoV R' (3) with po constant. a) Show that the total charge in the sphere is Qo = T POR³. b) Find the E-field at a point , = xâ outside the sphere ( > R). c) Find E at a point r, = rŷ inside the sphere d) Find the electric potential V just outside the sphere.