Gauss Law

Step 1: Understanding the Concept:
This problem is a direct application of Gauss's Law of electrostatics. Gauss's Law states that the total electric flux ( $%5CPhi$ ) through any closed surface is equal to the total net electric charge ( $Q_%7B%5Ctext%7Bin%7D%7D$ ) enclosed within that surface, divided by the permittivity of free space ( $%5Cepsilon_0$ ).

Step 2: Key Formula or Approach:
According to Gauss's Law:
$%5CPhi%20%3D%20%5Cfrac%7BQ_%7B%5Ctext%7Bin%7D%7D%7D%7B%5Cepsilon_0%7D$ To find the total charge inside the cube, we can rearrange the formula:
$Q_%7B%5Ctext%7Bin%7D%7D%20%3D%20%5CPhi%20%5Ctimes%20%5Cepsilon_0$

Step 3: Detailed Explanation:
Given:
Net electric flux, $%5CPhi%20%3D%201.05%20%5C%2C%20%5Ctext%7BN%20m%7D%5E2%20%5Ctext%7BC%7D%5E%7B-1%7D$
Permittivity of free space, $%5Cepsilon_0%20%3D%208.85%20%5Ctimes%2010%5E%7B-12%7D%20%5C%2C%20%5Ctext%7BC%7D%5E2%20%5Ctext%7BN%7D%5E%7B-1%7D%20%5Ctext%7Bm%7D%5E%7B-2%7D$
Now, we calculate the total charge enclosed, $Q_%7B%5Ctext%7Bin%7D%7D$ :
$Q_%7B%5Ctext%7Bin%7D%7D%20%3D%20(1.05%20%5C%2C%20%5Ctext%7BN%20m%7D%5E2%20%5Ctext%7BC%7D%5E%7B-1%7D)%20%5Ctimes%20(8.85%20%5Ctimes%2010%5E%7B-12%7D%20%5C%2C%20%5Ctext%7BC%7D%5E2%20%5Ctext%7BN%7D%5E%7B-1%7D%20%5Ctext%7Bm%7D%5E%7B-2%7D)$ $Q_%7B%5Ctext%7Bin%7D%7D%20%3D%209.2925%20%5Ctimes%2010%5E%7B-12%7D%20%5C%2C%20%5Ctext%7BC%7D$ Rounding to two decimal places, we get:
$Q_%7B%5Ctext%7Bin%7D%7D%20%5Capprox%209.29%20%5Ctimes%2010%5E%7B-12%7D%20%5C%2C%20%5Ctext%7BC%7D$

Step 4: Final Answer:
The total charge inside the cube will be $9.29%20%5Ctimes%2010%5E%7B-12%7D$ C.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Gauss Law

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs