Question

A uniform charge density of 500 nC/m3 is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

Answer 1

3.61581 Nm²/C

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

`\rho` = Charge density = 500 nC/m³

v = Volume =
`0.04^3\ m^3`

From Gauss' Law we have

`\phi=(Q)/(\epsilon)\\\Rightarrow \phi=(\rho v)/(\epsilon)\\\Rightarrow \phi=(500* 10^(-9)* 0.04^3)/(8.85* 10^(-12))\\\Rightarrow \phi=3.61581\ Nm^2/C`

The electric flux through this surface is 3.61581 Nm²/C