Question

?_E = ? E ? dA = q_{in}/?_0 , F_e = qE , F_e = 1/(4??_0) |q_1||q_2|/r^2 r? , ?_0 = 8.85 × 10^{-12} C^2/(N ? m^2) , q = ? ? ? 4?r^2dr Problem 1: A solid insulating sphere (Figure below on the left) with a radius of a carries a uniform volume charge density of ?. (a) What is Q, the total charge of the sphere? Hint: The total charge Q can be found by integrating ? over the entire volume of the sphere: Q = ? ?dV , where dV = 4?r^2dr for a spherical shell. Answer: Q = (4??a^3)/3. (b) What is the the Electric field at a distance of r < a from the center of the sphere. Answer: E? = (?r/3?_0)r?. (c) What is the the Electric field at a distance of r > a from the center of the sphere. Answer: E? = (?a^3/3?_0r^2)r?. (d) Make a sketch of the Electric-Field as a function of r. Answer: See Figure below on the right.

          ?_E = ? E ? dA = q_{in}/?_0 , F_e = qE , F_e = 1/(4??_0) |q_1||q_2|/r^2 r? , ?_0 = 8.85  × 10^{-12} C^2/(N ? m^2) , q = ? ? ? 4?r^2dr
Problem 1: A solid insulating sphere (Figure below on the left) with a radius of a carries a uniform volume charge density of ?. (a) What is Q, the total charge of the sphere? Hint: The total charge Q can be found by integrating ? over the entire volume of the sphere: Q = ? ?dV , where dV = 4?r^2dr for a spherical shell. Answer: Q = (4??a^3)/3.
(b) What is the the Electric field at a distance of r < a from the center of the sphere. Answer: E? = (?r/3?_0)r?.
(c) What is the the Electric field at a distance of r > a from the center of the sphere. Answer: E? = (?a^3/3?_0r^2)r?.
(d) Make a sketch of the Electric-Field as a function of r. Answer: See Figure below on the right.

?E = ? E ? dA = qin/?0 , Fe = qE , Fe = 1/(4??0) |q1||q2|/r^2 r? , ?0 = 8.85 × 10^-12 C^2/(N ? m^2) , q = ? ? ? 4?r^2dr
Problem 1: A solid insulating sphere (Figure below on the left) with a radius of a carries a uniform volume charge density of ?. (a) What is Q, the total charge of the sphere? Hint: The total charge Q can be found by integrating ? over the entire volume of the sphere: Q = ? ?dV , where dV = 4?r^2dr for a spherical shell. Answer: Q = (4??a^3)/3.
(b) What is the the Electric field at a distance of r < a from the center of the sphere. Answer: E? = (?r/3?0)r?.
(c) What is the the Electric field at a distance of r > a from the center of the sphere. Answer: E? = (?a^3/3?0r^2)r?.
(d) Make a sketch of the Electric-Field as a function of r. Answer: See Figure below on the right.

Added by Steven O.

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