Question
A charge of +Q is distributed uniformly throughout an insulating cube of side a. The net flux through the cube is:
(Q)/(2epsilon_0)
0
(Q)/(6epsilon_0)
(Q)/(epsilon_0)
(Q)/(4epsilon_0)
(Q)/(2epsilon_0)
0
(Q)/(6epsilon_0)
(Q)/(epsilon_0)
(Q)/(4epsilon_0)
Answers
GPT-4o mini
To determine the electric flux through a cube with a uniformly distributed charge of +Q, we can use Gauss's law. Gauss's law states that the electric flux \(\Phi_E\) through a closed surface is equal to the charge enclosed \(Q_{\text{enc}}\) divided by the permittivity of free space \(\epsilon_0\):
\[
\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}
\]
In this case, the closed surface is the cube, and since the entire charge +Q is uniformly distributed throughout the cube, the charge enclosed by the Gaussian surface (the cube) is Q.
Thus, applying Gauss's law:
\[
\Phi_E = \frac{Q}{\epsilon_0}
\]
Therefore, the net electric flux through the cube is:
\[
\frac{Q}{\epsilon_0}
\]
So the correct answer is:
\(\frac{Q}{\epsilon_0}\).
\[
\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}
\]
In this case, the closed surface is the cube, and since the entire charge +Q is uniformly distributed throughout the cube, the charge enclosed by the Gaussian surface (the cube) is Q.
Thus, applying Gauss's law:
\[
\Phi_E = \frac{Q}{\epsilon_0}
\]
Therefore, the net electric flux through the cube is:
\[
\frac{Q}{\epsilon_0}
\]
So the correct answer is:
\(\frac{Q}{\epsilon_0}\).