Question

Four charges $2\mu\text{C}, -3\mu\text{C}, 4\mu\text{C}, -4\mu\text{C}$ and $-1\mu\text{C}$ are enclosed by the Gaussian surface of radius $2\text{ m}$ . Net outward flux through the Gaussian surface is (in $\mu\text{V} - \text{m}$ ) [ $\epsilon_0 =$ permittivity of free space]}

• A. $\frac{2}{\epsilon_0}$
• B. zero
• C. $\frac{3}{\epsilon_0}$
• D. $\frac{5}{\epsilon_0}$

Hint:

In Gauss's law, radius of Gaussian surface does not matter for total flux. Only net enclosed charge matters.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
According to Gauss's Law, the total electric flux through a closed surface is equal to the net enclosed charge divided by the permittivity of the medium.
Step 2: Key Formula or Approach:
Gauss's Law: $\Phi = \frac{Q_{enclosed}}{\epsilon_0}$.
Step 3: Detailed Explanation:
Calculate the net enclosed charge $Q_{net}$:
\[ Q_{net} = 2 - 3 + 4 - 4 - 1 = -2\mu\text{C} \]
The magnitude of the net outward flux is:
\[ |\Phi| = \frac{|Q_{net}|}{\epsilon_0} = \frac{2}{\epsilon_0} \]
Step 4: Final Answer:
The net outward flux is $\frac{2}{\epsilon_0}$.