Four closed surfaces, S1 through S4, together with the charges
-2Q , Q , and -Q are sketched in the figure. (The colored lines
are the intersections of the surfaces with the page.) Find the
electric flux through each surface.
Unfortunately you an not copy and paste to pages on this site.
however remember Gauss !
To find the electric flux through each surface, we need to use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the electric charge enclosed divided by the electric permittivity of free space (ε₀).
1. Let's start with surface S1. The electric flux through a closed surface is given by Φ₁ = Q₁ / ε₀, where Q₁ is the charge enclosed by surface S1. In this case, S1 encloses the charge -2Q, so Φ₁ = (-2Q) / ε₀ = -2Q / ε₀.
2. Moving on to surface S2. The electric flux through this surface is given by Φ₂ = Q₂ / ε₀, where Q₂ is the charge enclosed by surface S2. In this case, S2 does not enclose any charge, so Φ₂ = 0.
3. Now let's consider surface S3. The electric flux through this surface is given by Φ₃ = Q₃ / ε₀, where Q₃ is the charge enclosed by surface S3. In this case, S3 encloses the charge Q, so Φ₃ = Q / ε₀.
4. Finally, let's calculate the electric flux through surface S4. Similar to the previous cases, the electric flux through this surface is given by Φ₄ = Q₄ / ε₀, where Q₄ is the charge enclosed by surface S4. In this case, S4 encloses the charge -Q, so Φ₄ = (-Q) / ε₀ = -Q / ε₀.
To summarize:
Φ₁ = -2Q / ε₀
Φ₂ = 0
Φ₃ = Q / ε₀
Φ₄ = -Q / ε₀
Note: The magnitude of the electric flux gives an indication of the amount of electric field passing through the surface, while the positive/negative sign indicates the direction of the electric field.