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

To find the electric flux through the surface \( S \) due to the given configuration of charges, we apply Gauss's Law. Gauss's Law states that the total electric flux \( \Phi_E \) through a closed surface is equal to the net charge enclosed \( Q_{\text{enc}} \) divided by the permittivity of free space \( \epsilon_0 \):

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

In this problem, you have five charges: +q, +5q, –2q, +3q, and –4q. It is given that the surface \( S \) encloses the charges +q, +5q, and –2q. Let's calculate the net charge within the surface:

• Charge +q
• Charge +5q
• Charge –2q

So, the total enclosed charge \( Q_{\text{enc}} \) is:

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

Substitute this back into Gauss's Law:

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

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

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

Answer 2

According to Gauss’s law, the electric flux Φ through a closed surface is given by:

\(Φ = \frac{q_{in}}{\epsilon_0}\),

where q_in is the total charge enclosed by the surface.

In this problem, the charges enclosed by the surface are \(q_{in} = q + (-2q) + 5q = 4q\).

Thus, the electric flux is:

\(Φ = \frac{4q}{\epsilon_0}\).

The correct answer is Option (2).