Question

Five charges \( +q, +5q, -2q, +3q \) and \( -4q \) are situated as shown in the figure. The electric flux due to this configuration through the surface S is: 

• A. \( \frac{5q}{\epsilon_0} \)
• B. \( \frac{4q}{\epsilon_0} \)
• C. \( \frac{3q}{\epsilon_0} \)
• D. \( \frac{q}{\epsilon_0} \)

Hint:

Gauss’s Law states that the total electric flux through a closed surface depends only on the net charge enclosed within the surface.

Answer 1

The Correct Option is B

Step 1: Gauss's Law Application
Gauss's Law states that the total electric flux \( \Phi_E \) through a closed surface is calculated as: \[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} \] Here, \( Q_{\text{enc}} \) represents the total charge contained within the closed surface.
Step 2: Net Enclosed Charge Determination
The charges located within the closed surface are: \[ q, -2q, +5q \]Their summation yields: \[ Q_{\text{enc}} = q + (-2q) + 5q = 4q \]
Step 3: Flux Calculation
Applying Gauss's Law: \[ \Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0} = \frac{4q}{\epsilon_0} \]Final Result: The electric flux through the closed surface amounts to \( \frac{4q}{\epsilon_0} \).