Question

An electric point charge of Q = 22.5 nC is placed at the center of a cube with a side length of a = 16.3 cm. The cube in this question is only a mathematical object, it is not made out of any physical material. What is the electric flux through all six sides of the cube?

Answer 1

Answer:

The electric flux is  $\phi = 2.5 *10^{3} \ Nm^2 \cdot C^{-1}$

Explanation:

From the question we are told that

  The magnitude of the electric point charge  $q = 22.5 nC = 22.5 *10^{-9} \ C$

   The length of the one side of the cube is $l = 16.3 \ cm = 0.163 \ m$

   The number of  sides is  $N= 6$  

The electric flux according to Gauss law is mathematically evaluated as

          $\phi = \frac{q}{\epsilon_o}$

Where $\epsilon _ o$ is the permitivity of free space with value  $\epsilon_o = 8.85*10^{-12}\ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2$

  substituting values

        $\phi = \frac{22.5 *10^{-9}}{8.85 *10^{-12}}$

         $\phi = 2.5 *10^{3} \ Nm^2 \cdot C^{-1}$