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Figure 6
Answer the following.
Two Gaussian surfaces, S₁ and S₂ are shown in Figure 6 below. What is the ratio of electric flux…
Two Gaussian surfaces, $S_1$ and $S_2$ are shown in Figure 6 below.
(a)[1]
What is the ratio of electric flux emerging out of these two surfaces?
(b)[1]
What happens to this ratio if the space occupied by each Gaussian surface is doubled?
Answer
Answer (a)
By Gauss's law, $\phi = \frac{q_{enclosed}}{\epsilon_0}$. $S_1$ encloses $-2q + q = -q$ and $S_2$ encloses $2q + q = 3q$, so $\frac{\phi_1}{\phi_2} = \frac{-q}{3q} = -\frac{1}{3}$ (magnitudes in the ratio $1:3$).
Answer (b)
The ratio remains the same ($-\frac{1}{3}$), since the flux depends only on the charge enclosed and not on the size of the surface.