A solid insulating sphere of radius 5.00 cm has a uniform charge density through

Question

A solid insulating sphere of radius 5.00 cm has a uniform charge density throughout its volume Concentric with this sphere is a hollow conducting sphere whose inner and outer radii are 20.0 cm and 25.0 cm. Suppose the electric field at a point 10.0 cm from the center is measured to be 3.60 x 103 N/C radially inward and the electric field at a point 50.0 cm from the center is of magnitude 200 N/C and points radially outward. From this information, find the following: 4. a. b. C. d. The charge on the insulating sphere The net charge on the hollow conducting sphere The charge on the inner surface of the hollow conducting sphere The charge on the outer surface of the hollow conducting sphere

Explanation / Answer

4. from Gauss law,

Net flux = E ( 4 pi r^2) = Qin / e0

for r = 0.10 m , E = -3.60 x 10^3 N/C ,Qin = Q_sphere

(-3.60 x 10^3 )( 4pi 0.10^2)= Q_sphere / (8.854 x 10^-12)

Q_sphere = - 4 x 10^-9 C Or - 4 nC ....Ans

(B) for r = 0.50 m , E = 200 N/C

Qin = Q_sphere + Q_hollow

- 4nC + Q_hollow = 5.56 nC  

Q_hollow = 9.56 nC or 9.56 x 10^-9 C ....Ans

(C) Qinner + Qsphere = 0

Q_inner = 4 nC

(D) 4 + Q_outer = 9.56 nC

Q_outer = 5.56 nC

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