A spherical shell contains three charged objects. The first and second objects have a charge of −18.0 nC−18.0 nC and 38.0 nC38.0 nC , respectively. The total electric flux through the shell is −218 N⋅m2/C−218 N⋅m2/C . What is the charge on the third object?

q3 = 21.9 nC

Explanation:

By the Gauss theorem you have that the electric flux in a Gaussian surface is given by:

     (1)

ФE: electric flux = -218Nm^2/C

Q: net charge inside the Gaussian surface

εo: dielectric permittivity of vacuum = 8.85*10^-12 C^2/(Nm^2)

You can consider the spherical shell as a Gaussian surface. Then, the net charge inside the surface is:

    (2)

where charge q3 is unknown charge of the third object:

You replace the equation (2) into the equation (1), and you solve for q3:

hence, the charge of the third object is 21.9 nC

r = ρ x length / area  

ρ = r x area / length  

ρ is in ohm-meters  

in basic units, it is m³kg/s³a²  

i think this is it.