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

The electric flux is
`\phi = 2.5 *10^(3) \ Nm^2 \cdot C^(-1)`

Step-by-step 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 = (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 = (22.5 *10^(-9))/(8.85 *10^(-12))`

`\phi = 2.5 *10^(3) \ Nm^2 \cdot C^(-1)`