The net electric flux through a Gaussian surface is −680 N · m2/C. What is the net charge of the source inside the surface?
nC
qin= (φE/ε =
To find the net charge of the source inside the Gaussian surface, we can use Gauss's Law, which states that the net electric flux through a closed surface is equal to the net charge enclosed divided by the electric constant (ε₀).
Mathematically, Gauss's Law is given by:
Φ = Q_enclosed / ε₀
Where:
Φ is the net electric flux through the Gaussian surface.
Q_enclosed is the net charge enclosed by the Gaussian surface.
ε₀ is the electric constant, approximately equal to 8.85 x 10⁻¹² N m²/C².
Given that the net electric flux through the Gaussian surface is -680 N m²/C, we can substitute this value into the equation:
-680 N m²/C = Q_enclosed / ε₀
Now, we'll rearrange the equation to solve for Q_enclosed:
Q_enclosed = Φ * ε₀
Substituting the given values:
Q_enclosed = -680 N m²/C * (8.85 x 10⁻¹² N m²/C²)
Calculating this expression:
Q_enclosed ≈ -6.018 N m²/C²
Finally, the net charge of the source inside the Gaussian surface is approximately -6.018 nC (nanoCoulombs).
To find the net charge of the source inside the Gaussian surface, you can use Gauss's Law, which states that the net electric flux through a closed surface is directly proportional to the net charge enclosed by the surface.
The formula for Gauss's Law is:
Φ = q / ε₀
Where:
Φ is the net electric flux through the surface,
q is the net charge enclosed by the surface, and
ε₀ is the permittivity of free space (ε₀ = 8.854 x 10^-12 C^2/Nm^2).
In this case, we are given that the net electric flux through the Gaussian surface is -680 N·m²/C.
Rearranging the formula, we can solve for the net charge enclosed by the surface:
q = Φ * ε₀
Plugging in the given values:
q = -680 N·m²/C * 8.854 x 10^-12 C²/N·m²
Now, let's calculate the value:
q = -6.01232 x 10^-9 C
So, the net charge of the source inside the Gaussian surface is approximately -6.01232 nanoCoulombs (nC).