Question

A single point charge is placed at the center of an imaginary cube that has 10 cm long edges. The electric flux out of one of the cube's sides is -1 kN·m^2/C. How much charge is at the center?

Answer 1

Step-by-step explanation:

Given:

Length of each side of the cube,
`L=10\ cm`

The Elecric flux through one of the side of the cube is,
`\phi =-1 kNm^2/C.`

The net flux through a closed surface is defined as the total charge that lie inside the closed surface divided by
`\epsilon_0`

Since Flux is a scalar quantity. It can added to get total flux through the surface.

`\phi_(total)=(Q_(in))/(\epsilon_0)\\6* {-1}* 10^3=(Q_(in))/(\epsilon_0)\\\\Q_(in)=-6}* 10^3\epsilon_0\\Q_(in)=-6}* 10^3*8.85* 10^(-12)\\Q_(in)=-53.1*10^(-9)\ C`

So the the charge at the centre is calculated.