The Electric Flux and Total Charge Enclosed by a Cubical Box

Calculating the Total Charge Enclosed

The electric flux through a cubical box 8.0 cm on a side is (1.2 × 10³ N⋅m²/C). What is the total charge enclosed by the box?

Final answer:

The total charge enclosed by the cubical box can be found by multiplying the electric flux by the permittivity of free space. In this case, the total charge enclosed is approximately 1.062 × 10⁻⁸ C.

Explanation:

The electric flux through a closed surface is given by the product of the electric field and the area of the surface. In this case, a cubical box with sides of 8.0 cm has an electric flux of 1.2 × 10³ N·m²/C. To find the total charge enclosed by the box, we can use Gauss's Law.

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

So, to find the total charge enclosed, we need to multiply the electric flux by the permittivity of free space. The permittivity of free space, ε₀, is approximately 8.85 × 10⁻¹² N⁻¹·m⁻²·C². Multiplying the electric flux by ε₀ gives us the total charge enclosed.

Therefore, the total charge enclosed by the box is (1.2 × 10³ N·m²/C) × (8.85 × 10⁻¹² N⁻¹·m⁻²·C²) = 1.062 × 10⁻⁸ C.