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

Concept:
By Gauss's law: \[ \Phi = \frac{q_{\text{enclosed}}}{\epsilon_0} \] ip

Step 1: Add all enclosed charges.
\[ q_{\text{net}}=2-3+4-4-1 \] \[ q_{\text{net}}=-2\mu\text{C} \] ip

Step 2: Use Gauss's law.
\[ \Phi=\frac{-2\mu\text{C}}{\epsilon_0} \] So the net outward flux is negative. Thus mathematically the flux is: \[ -\frac{2}{\epsilon_0} \] Since this value does not appear in the options, the keyed option in the source is inconsistent with the arithmetic. ip The direct calculation gives:
\[ \boxed{-\frac{2}{\epsilon_0}} \]