A solid conducting sphere of radius 0.100 m bears a net charge of Q_1, net = +5.

Question

A solid conducting sphere of radius 0.100 m bears a net charge of Q_1, net = +5.50 times 10^-6 C. Concentric with the sphere is a conducting spherical shell having an inner radius of0.400 m and an outer radius of 0.500 m. The spherical shell bears a net charge of Q_2, net = -7.50 times 10^-6 C. A second conducting spherical shell bearing an unknown charge surrounds the conductors previously described and is concentric with them. If point P_1 is 0.0500 m from the center of the solid conducting sphere, what is the electric field strength at point P_1? 0 N/C 4.09 times 10^4 N/C 5.58 times 10^4 N/C 1.20 times 10^5 N/C If point P_2 is 0.250 m from the center of the solid conducting sphere, what is the electric field strength at point P_2? 6.73 times 10^5 N/C 7.22 times 10^5 N/C 7.91 times 10^5 N/C 9.07 times 10^5 N/C What is the surface charge density on the outer surface of the middle conductor, i.e., what is the surface charge density on the spherical surface of radius 0.500 m? +3.26 times 10^-7 C/m +2.24 times 10^-7 C/m^2 -5.44 times 10^-7 C/m^2 -6.37 times 10^-7 C/m^2 -7.04 times 10^-7 C/m^2

Explanation / Answer

9)

r1 = 0.05 < 0.1 m

consider a gassian sphere of radis r1

the sharge inside the sphere = 0

electric field E1 = k*Q/r1^2 = 0

OPTION (A)

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10)

at point P2

E2 = k*Q1net/r2^2

E2 = 9*10^9*5.5*10^-6/0.25^2

E2 = 7.91*10^5 N/C

option (C)

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11)

Qinner + Qouter = -7.5*10^-6

Qinner = -5.5*10^-6

Qouter = -7.5*10^-6 + 5.5*10^-6 = -2*10^-6 C

surface charge density = Qouter/(4*pi*Router^2)

surface charge density = -2*10^-6/(4*pi*0.5^2) = -6.37*10^-7 C/m^2

option (D)

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