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. \( \frac{q}{\epsilon_0} \)

Answer 1

The Correct Option is B

Gauss's Law is applied to determine the electric flux through surface \( S \). The law states that the total electric flux \( \Phi_E \) through a closed surface equals the enclosed net charge \( Q_{\text{enc}} \) divided by the permittivity of free space \( \epsilon_0 \):

\(\Phi_E = \frac{Q_{\text{enc}}}{\epsilon_0}\)

The problem provides five charges: +q, +5q, –2q, +3q, and –4q. Surface \( S \) encloses charges +q, +5q, and –2q. The net charge enclosed is calculated as follows:

• Charge +q
• Charge +5q
• Charge –2q

The total enclosed charge \( Q_{\text{enc}} \) is:

\({Q_{\text{enc}} = q + 5q - 2q = 4q}\)

Substituting this into Gauss's Law yields:

\(\Phi_E = \frac{4q}{\epsilon_0}\)

Therefore, the electric flux through surface \( S \) is \(\frac{4q}{\epsilon_0}\).

The correct option is \(\frac{4q}{\epsilon_0}\).