(g) From part (f), what must be the charge on the outer surface of the hollow sphere? Qouter 1 A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε 0, a, b, c and r. Do not substitute numerical values; use variables only.) Insulator Conductor (a) Find the charge contained within a sphere of radius r < a. qin = 1 (b) From this value, find the magnitude of the electric field for r < a. E = 1 (c) What charge is contained within a sphere of radius r when a < r < b? ain = 1 × (d) From this value, find the magnitude of the electric field for r when a < r < b. E = 1 (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r? E = 1 (f) From this value, what must be the charge on the inner surface of the hollow sphere? Qinner = 1 ×

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(g) From part (f), what must be the charge on the outer surface of the hollow sphere?
Qouter
1
Transcribed Image Text:(g) From part (f), what must be the charge on the outer surface of the hollow sphere? Qouter 1
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged,
conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric
fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε 0, a, b, c and r. Do not substitute numerical values; use variables only.)
Insulator
Conductor
(a) Find the charge contained within a sphere of radius r < a.
qin
=
1
(b) From this value, find the magnitude of the electric field for r < a.
E = 1
(c) What charge is contained within a sphere of radius r when a < r < b?
ain
=
1
×
(d) From this value, find the magnitude of the electric field for r when a < r < b.
E = 1
(e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r?
E =
1
(f) From this value, what must be the charge on the inner surface of the hollow sphere?
Qinner
=
1
×
Transcribed Image Text:A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε 0, a, b, c and r. Do not substitute numerical values; use variables only.) Insulator Conductor (a) Find the charge contained within a sphere of radius r < a. qin = 1 (b) From this value, find the magnitude of the electric field for r < a. E = 1 (c) What charge is contained within a sphere of radius r when a < r < b? ain = 1 × (d) From this value, find the magnitude of the electric field for r when a < r < b. E = 1 (e) Now consider r when b < r < c. What is the magnitude of the electric field for this range of values of r? E = 1 (f) From this value, what must be the charge on the inner surface of the hollow sphere? Qinner = 1 ×
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