(8c23p49) In the figure (b), a nonconducting spherical shell, of inner radius a

Question

(8c23p49) In the figure (b), a nonconducting spherical shell, of inner radius a = 17.2 cm and outer radius b = 22.2 cm, has a volume charge density ? = A/r (within its thickness), where A is a constant and r is the distance from the center of the shell. In addition, a point charge q = 5.00?10-5 C is located at the center. What value should A have if the electric field in the shell (a < r < b) is to be uniform? (Hint : The constant A depends on a but not on b.) Incorrect. Tries 1/10 Previous Tries What is the value of E?

Explanation / Answer

a)

E1 = Qnet/(4??r^2)

Qnet = ??(4?r^2)dr

Integration from "a" to "r":

Qnet = ??(4?r^2)dr = ?(A/r)(4?r^2)dr

Qnet = ?(A)(4?r)dr = 2A?r^2 - 2A?a^2

therefore:

E1 = Qnet/(4??r^2) = (2A?r^2 - 2A?a^2)/(4??r^2)

E1 = (Ar^2 - Aa^2)/(2?r^2) = A/(2?) - (Aa^2)/(2?r^2)

E2 = q/(4??r^2)

E1 + E2 = c = constant

A/(2?) - (Aa^2)/(2?r^2) + q/(4??r^2) = c

Therefore:

(Aa^2)/(2?r^2) = q/(4??r^2)

>>>>>> A = q/(2?a2) = 5e-5/(2*3.1416*0.172*0.172)

>>>>>> A = 2.69e-4 C/m2

b)

E1 + E2 = c = constant

A/(2?) - (Aa^2)/(2?r^2) + q/(4??r^2) = c

Therefore:

c = A/(2?) = 2.69e-4/(2*8.85e-12) = 1.52e7 N/C

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