Question

A uniform charge density of 500nC/m^3 is distributed throughout a spherical volume (radius 16cm). Consider a cubical (4cm along each edge) surface completely inside the sphere. Determine the electric flux through the surface of the cube.

Answer 1

Answer:

$3.61581\ Nm^2/C$

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

V = Volume of cube = $0.04^3$

$\rho$ = Charge density = $500\ nC/m^3$

Electric flux is given by

$\phi=\dfrac{Q}{\epsilon_0}\\\Rightarrow \phi=\dfrac{\rho V}{\epsilon_0}\\\Rightarrow \phi=\dfrac{500\times 10^{-9}\times 0.04^3}{8.85\times 10^{-12}}\\\Rightarrow \phi=3.61581\ Nm^2/C$

The electric flux through the surface of the cube is $3.61581\ Nm^2/C$