For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 c

Question

For the configuration shown in the figure below, suppose a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose the electric field at a point 14.0 cm from the center is measured to be 3.85 times 10^3 N/C radially inward and the electric field at a point 50.0 cm from the center is of magnitude 211 N/C and points radially outward. From this information, find the following. (Include the sign of the charge in your answer.) 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

part(a)

consider a gaussian sphere of radius r = 14 cm = 0.14 m

flux = E*A = E*4*pi*r^2

from gauss law flux = Q/e0

-E*4*pi*r^2 = Q/e0

Q = E*4*pi*r^2*e0

Q = -3.85*10^3*4*pi*0.14^2*8.85*10^-12

Q = -8.4*10^-9 C

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b)

at r > c

electric field E = k(Q+Qnet)/r^2

given E = 211 N/C

211 = 9*10^9*(-8.4*10^-9+Qnet)/0.5^2

Qnet = 1.43*10^-8 C

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part(c)

Qinner = -Q = +8.4*10^-9 C

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part(d)

Qnet = Qinner + Qouter

Qouter = Qnet - Qinner

Qouter = 1.43*10^-8 - 8.4*10^-9 = 5.9*10^-9 C

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