What Is the Net Flux Through Gaussian Surfaces Near a Charged Rod?

[musicfairy]

In the figure below, the charge on a neutral isolated conductor is separated by a nearby positively charged rod. What is the net flux through each of the five Gaussian surfaces shown in cross section? Assume that the charges enclosed by S₁, S₂, and S₃ are equal in magnitude.

Surface 1:

Surface 2:

Surface 3:

Surface 4:

Surface 5:



I don't know what to do, so I'll need someone(s) to guide me through the process.

I'm guessing I'll have to use the equations

Φ= q/ε₀

I really don't know this stuff well, so I can't show much work as of now. That's why I'm trying to find someone who's willing to explain to me a step at a time.

First of all how do I know what sign it is? If it's negative does it mean the sign of q/ε₀ is negative? Like S₂ would be −q/ε₀?

And for S₄ would Φ = 0 because it contains S₁ and S₂ and they have opposite charges?

 

[LowlyPion]

Figure that the net flux is the sum of the enclosed charge divided by permittivity.

So Φ= q/ε_o

So yes, S4 is 0 by the problem statement.

The others can be determined simply by using the formula.

I believe that S2 would be ΣΦ₂ = -q/ε_o as stated.

 

[musicfairy]

I think I get it now.

S₁: Φ= q/ε_o

S₂: Φ= −q/ε_o

S₃: Φ= q/ε_o

S₄: Φ= 0

S₅: Φ= 2q/ε_o


Is this correct?