Question

A sphere encloses charges \(+5\,C\) and \(-2\,C\), while a charge \(-3\,C\) is outside the sphere. What is the electric flux through the sphere?

• A. \(\dfrac{3C}{\varepsilon_{0}}\)
• B. \(-\dfrac{3C}{\varepsilon_{0}}\)
• C. Zero
• D. \(\dfrac{10C}{\varepsilon_{0}}\)

Hint:

For any closed Gaussian surface, \[ \boxed{\Phi=\frac{Q_{\text{enclosed}}}{\varepsilon_{0}}} \] Always calculate the net enclosed charge only. Remember: \[ \boxed{ \begin{aligned} \text{Positive enclosed charge} &\Rightarrow \text{Positive flux},\\ \text{Negative enclosed charge} &\Rightarrow \text{Negative flux},\\ \text{External charges} &\Rightarrow \text{No effect on net flux}. \end{aligned} } \]

Answer 1

The Correct Option is A

By Gauss's law, the total electric flux through a closed surface depends only on the charge enclosed within it. Here $Q_{enc} = +5 - 2 = +3$ C, so $\phi = Q_{enc}/\varepsilon_0 = 3/\varepsilon_0$ Nm²/C; the $-3$ C charge outside contributes nothing.