To calculate the electric flux through the imaginary sphere surrounding the point charge, we can use Gauss's Law. Gauss's Law states that the electric flux through any closed surface is equal to the charge enclosed divided by the permittivity of free space (ε₀).
The formula for electric flux through a closed surface is:
Φ = Qenc / ε₀
where Φ is the electric flux, Qenc is the charge enclosed by the surface, and ε₀ is the permittivity of free space.
In this case, the charge enclosed is the charge q itself, which is +6 nC (nanocoulombs). The permittivity of free space, ε₀, is approximately equal to 8.85 x 10^-12 C²/(N·m²).
So, substituting the values into the formula:
Φ = (6 nC) / (8.85 x 10^-12 C²/(N·m²))
Converting nanocoulombs to coulombs (1 nC = 10^-9 C):
Φ = (6 x 10^-9 C) / (8.85 x 10^-12 C²/(N·m²))
Simplifying:
Φ = (6 x 10^-9) / (8.85 x 10^-12 N·m²/C²)
Φ ≈ 6.78 x 10^2 N·m²/C
Therefore, the resulting electric flux through the imaginary sphere is approximately 6.78 x 10^2 N·m²/C.