Question

1. A 30 cm radius hollow spherical conductive shell of has a surface charge density of 10 µC/m2, a point charge Q1 is in its center. Find the electric flux through the spherical surface centered at Q1:

a. if the value is Q1= +3.5x10-6 C charge

b. if the value is Q1= -2.5x10-6 C charge

c. What would be the electric field in each case?

Please explain how you got the answer, having trouble understanding this and can't seem to picture it in my head. Thank you!

Answer 1

1) total charge on conductive sheel, Q2 = sigma*A

= 10*10^-6*(4*pi*0.3^2)

= 1.13*10^-5 C

a) Tota electric flux = Qin/epsilon

= (Q1 + Q2)/epsilon

= (3.5*10^-6 + 1.13*10^-5)/(8.854*10^-12)

= 1.67*10^6 N.m^2/C

b) Tota electric flux = Qin/epsilon

= (Q1 + Q2)/epsilon

= (-2.5*10^-6 + 1.13*10^-5)/(8.854*10^-12)

= 9.94*10^5 N.m^2/C

c) in case 1, E = k*(Q1+Q2)/r^2

= 9*10^9*((3.5*10^-6 + 1.13*10^-5)/0.3^2

= 1.48*10^6 N/c

in case 2, E = k*(Q1+Q2)/r^2

= 9*10^9*(-2.5*10^-6 + 1.13*10^-5)/0.3^2

= 8.80*10^6 N/c