If the net flux through a cube is 1.05 N m² C⁻¹, what will be the total charge inside the cube? (Given: The permittivity of free space is 8.85×10⁻¹² C² N⁻¹ m⁻²).

The correct option is 9.29 × 10⁻¹² C.

To find the total charge inside the cube, we can apply Gauss's Law. Gauss's Law states that the net electric flux ($\Phi$) passing through any closed surface is equal to the total charge ($q_{\text{enclosed}}$) enclosed by the surface divided by the permittivity of free space (${\epsilon }_0$).

$\Phi =\frac{q_{\text{enclosed}}}{{\epsilon }_0}$

Rearranging the formula to solve for the enclosed charge ($q_{\text{enclosed}}$):

$q_{\text{enclosed}}=\Phi \times {\epsilon }_0$

We are given the following values in the problem:
- Net electric flux, $\Phi =1.05{\text{N m}}^2{\text{C}}^{-1}$
- Permittivity of free space, ${\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$

Substitute these values into the rearranged equation:

$q_{\text{enclosed}}=1.05\times (8.85\times {10}^{-12})$

Now, perform the calculation:

$q_{\text{enclosed}}=9.2925\times {10}^{-12}\text{C}$

Rounding this to three significant figures gives:
$q_{\text{enclosed}}\approx 9.29\times {10}^{-12}\text{C}$

Therefore, the total charge inside the cube is 9.29 × 10⁻¹² C.