Point charges of 2μC and -5μC is at an unspecified location inside a cube with a side of 50cm. Find the net electric flux through the surfaces of the cube.

The net electric flux through any closed surface is given by Gauss's Law, which states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀).

The formula for Gauss's Law is:

Φ = Q / ε₀

Where:

• Φ is the electric flux,
• Q is the total charge enclosed by the surface,
• ε₀ is the permittivity of free space, which is approximately 8.85 x 10^-12 C²/N·m².

In this case, the total charge enclosed by the cube is the sum of the two point charges, which is 2μC - 5μC = -3μC = -3 x 10^-6 C.

Substituting these values into Gauss's Law gives:

Φ = (-3 x 10^-6 C) / (8.85 x 10^-12 C²/N·m²) = -339.0 x 10^6 N·m²/C

Therefore, the net electric flux through the surfaces of the cube is -339.0 x 10^6 N·m²/C.