Question

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?

Answer 1

Answer:

q3 = 21.9 nC

Explanation:

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

$\Phi_E=\frac{Q}{\epsilon_o}$      (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:

$Q=-18.0nC+38.0nC+q_3$     (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:

$\epsilon_0 \Phi_E=-18.0*10^{-9}C+38.0*10^{-9}C+q_3\\\\\epsilon_0 \Phi_E=20*10^{-9}C+q_3\\\\q_3=(8.85*10^{-12}C^2/(Nm^2))(-218Nm^2/C)-20*10^{-9}C\\\\q_3=2.19*10^{-9}C=21.9nC$

hence, the charge of the third object is 21.9 nC