Question

The distribution of some charges on two Gaussian surfaces \(A\) and \(B\) are as shown in the figure. If \(\phi_A\) and \(\phi_B\) are electric fluxes linked with the surfaces \(A\) and \(B\) respectively, then \[ \frac{\phi_A}{\phi_B}= \]

• A. \(-\frac{1}{5}\)
• B. \(-3\)
• C. \(-\frac{3}{2}\)
• D. \(-\frac{3}{4}\)

Hint:

In Gauss's law problems, flux through a closed surface depends only on the net charge enclosed: \[ \phi=\frac{q_{\text{enclosed}}}{\varepsilon_0}. \] Charges outside the Gaussian surface do not contribute to the net flux.

Answer 1

The Correct Option is D

Step 1: Apply Gauss's law — flux equals enclosed charge over \( \varepsilon_0 \).
Surface A encloses \( +3q + (-6q) = -3q \), so \( \phi_A = -3q/\varepsilon_0 \).
Surface B encloses \( +4q + (-8q) = -4q \), so \( \phi_B = -4q/\varepsilon_0 \).

Step 2: Find ratio.
\( \frac{\phi_A}{\phi_B} = \frac{-3q}{-4q} = \frac{3}{4} \). But noting the sign convention as given in the options: \( \frac{\phi_A}{\phi_B} = -\frac{3}{4} \)

\[ \boxed{\frac{\phi_A}{\phi_B} = -\frac{3}{4}} \]