Rectifying my logic of Gauss's Law

In summary, the conversation discusses a problem involving Gauss's Law and the charge distribution on the surfaces of two concentric shells. The attempted solution initially calculates the total charge on the outer surface to be 94.9 μC, but after a hint, the correct answer is determined to be 91.6 μC, taking into account the charge on the inner surface of the larger shell. The final clarification is made that the question is specifically asking for the charge on the outer surface, not the total charge of the larger shell.
  • #1
The Blind Watchmaker
17
0

Homework Statement


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Homework Equations


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The Attempt at a Solution


E4Πr2 = Q/∈0
49000⋅4Π4.12 =Q/∈0
Q = 91.6 μC
Qshell = Q = 91.6 μC
Qshell = Qinner + Qouter
91.6 = -3.3 + Qouter
Qouter = 94.9 μC

Can someone point out the error? I have skipped too many lectures and I am catching up right now. Any help would be appreciated! :)
 

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  • #2
Pay close attention to the actual question posed! Precisely what charge are they going for?
 
  • #3
gneill said:
Pay close attention to the actual question posed! Precisely what charge are they going for?
Ah I think I get it. Since the electric field inside a conductor must be 0, there must exist a charge on the inner surface of the larger shell that is equal and opposite to 3.3 μC. Thus, the remaining charge is 91.6 - 3.3 = 88.3 μC. Is this what you are hinting at?
 
  • #4
The Blind Watchmaker said:
Ah I think I get it. Since the electric field inside a conductor must be 0, there must exist a charge on the inner surface of the larger shell that is equal and opposite to 3.3 μC. Thus, the remaining charge is 91.6 - 3.3 = 88.3 μC. Is this what you are hinting at?
Something like that, but take care... Sure, the inner shell's charge is matched and effectively "cancelled" by the charge on the inner surface of the outer shell. So what remains on the outer surface must be what Gauss's Law "sees" as the contained charge...
 
  • #5
gneill said:
Something like that, but take care... Sure, the inner shell's charge is matched and effectively "cancelled" by the charge on the inner surface of the outer shell. So what remains on the outer surface must be what Gauss's Law "sees" as the contained charge...
So if the question is asking for the "charge of the larger shell" it would be 91.6 + 3.3 μC, but since this question is only asking for the outer surface, the charge is taken to be 91.6 μC?
 
  • #6
The Blind Watchmaker said:
So if the question is asking for the "charge of the larger shell" it would be 91.6 + 3.3 μC, but since this question is only asking for the outer surface, the charge is taken to be 91.6 μC?
Right!
 
  • #7
gneill said:
Right!
It is 3 AM here but thanks!
 

1. What is Gauss's Law?

Gauss's Law is a fundamental law in electromagnetism that describes the relationship between electric charges and the electric field they produce.

2. How is Gauss's Law used to rectify logic?

Gauss's Law can be used to rectify logic by providing a framework for understanding and solving problems related to electric charges and their interactions. By following the mathematical principles of Gauss's Law, one can arrive at logical and consistent conclusions.

3. What are the key components of Gauss's Law?

The key components of Gauss's Law are the electric flux, which is a measure of the amount of electric field passing through a given surface, and the electric charge enclosed within that surface.

4. How does Gauss's Law help us understand electric fields?

Gauss's Law helps us understand electric fields by providing a mathematical relationship between electric charges and the electric field they produce. It allows us to calculate the strength and direction of the electric field at any point in space.

5. Can Gauss's Law be applied to all situations involving electric charges?

Yes, Gauss's Law is a general law that can be applied to all situations involving electric charges. However, it is most useful for situations with high levels of symmetry, as it simplifies the calculations and allows for easier application of the law.

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