Is Zero Electric Field on a Closed Surface Indicative of No Net Charge?

Remember, the net charge enclosed by a surface dictates the electric field on that surface. So what can you say about the net charge enclosed by the inner and outer surfaces of the conductor?In summary, the conversation discusses various concepts related to electric fields, charge distribution, and Gauss's Law. It explores the relationship between electric field and net charge enclosed, as well as the impact of charge distribution on the electric field. It also touches on the concept of sources and sinks in gravitational and electric fields. Additionally, the conversation delves into the effects of changing the shape of an object on its electric field and the application of Gauss's Law to calculate electric fields.
  • #1
willdefender
7
0
QUESTIONS
5.The electric field E is zero at all points on a closed surface; is there necessarily no net charge within the surface? If a surface encloses zero net charge, is the electric field necessarily zero at all points on the surface?

6.Define gravitational flux in analogy to electric flux. Are there "sources" and "sinks" for the gravitational field as there are for the electric field?

8.A spherical basketball(a nonconductor) is given a charge Q distributed uniformly over its surface.What can you say about the electric field inside the ball? A person now steps on the ball, collapsing it, and forcing most of the air out without altering the charge. What can you say about the field inside now?

12.A conductor carries a net positive charge Q. There is a hollow cavity within the conductor, at whose center is a negative point charge -q. What is the charge on (a)the outer surface of the conductor and (b) the inner surface of the conductor?


ATTEMPT
5.----I think the first one is yes because according to Gauss's Law, if a surface enclose net charge, E at points on surface would not be 0; as for the last one, I think it is wrong because even though there is no sinks or sources in a closed surface, electric field lines are still allowed to pass through the surface, which results that E at some points on the surface is not 0.

6.----I think anything that has mass can be considered as "sinks", but how about "sources"?

8.----At first, the field is determined the Gauss's Law. After collapsing, the field doesn't change because of no loss of charge.

12.----I think both are 0. For the outer surface, the net charge it enclose is 0, so that E on the surface is 0.
 
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  • #2
5. Sounds good
6. Right; so what do you think about sources?
8. Yes, the field is determined by Gauss's law at first. So what can you say about its value inside the basketball? Afterwards, note that the basketball is no longer spherical.
12. Why would you say the net charge enclosed in the outer surface is 0? Think about this: what is the electric field in any region filled by conducting material?
 
  • #3
diazona said:
5. Sounds good
6. Right; so what do you think about sources?
8. Yes, the field is determined by Gauss's law at first. So what can you say about its value inside the basketball? Afterwards, note that the basketball is no longer spherical.
12. Why would you say the net charge enclosed in the outer surface is 0? Think about this: what is the electric field in any region filled by conducting material?

Thanks for your replying!
6.If something that has a negative mass, it can be considered as a source.

8.So if the charge are in the ball(not distributed on the ball), the charge will not changed.But does not the electric field determined only by the charge? Does the distribution of charge affect that?

12.I think the net charge is 0, so...
Is the electric field in any region filled by conducting material 0?
 
  • #4
8. Yes, the electric field is determined by the charge distribution...

12. It's true that the electric field in any region filled by conducting material is 0. (Do you know why?) Now think about applying Gauss's law to a surface which runs through the conductor.
 
  • #5
diazona said:
8. Yes, the electric field is determined by the charge distribution...

12. It's true that the electric field in any region filled by conducting material is 0. (Do you know why?) Now think about applying Gauss's law to a surface which runs through the conductor.

8.We can calculate the previous field with E1=Q/(4*Π*ε0*r*r), after collasping, we should calculate it with E2=δ/(2*ε0）=E1/2, isn't it?

12. I think the charge on the outer surface is Q-q, while the one on the inner surface is q-Q.
 
  • #6
willdefender said:
8.We can calculate the previous field with E1=Q/(4*Π*ε0*r*r), after collasping, we should calculate it with E2=δ/(2*ε0）=E1/2, isn't it?
Inside the ball? That's not correct for E1. Or well, technically you could calculate it that way, but it would involve an integral that you don't really have to do. What happened to using Gauss's Law?
willdefender said:
12. I think the charge on the outer surface is Q-q, while the one on the inner surface is q-Q.
Nope, I don't believe that's correct.
 

FAQ: Is Zero Electric Field on a Closed Surface Indicative of No Net Charge?

What is Gauss's Law?

Gauss's Law is a fundamental law in physics that explains the relationship between the electric field and the distribution of electric charges. It states that the electric flux through any closed surface is equal to the net charge enclosed by that surface divided by the permittivity of free space.

How is Gauss's Law derived?

Gauss's Law is derived from Coulomb's Law, which describes the force between two point charges. By considering a small Gaussian surface around a point charge, and using the divergence theorem, it can be shown that the electric flux through the surface is equal to the charge enclosed divided by the permittivity of free space.

3. What is the significance of Gauss's Law?

Gauss's Law is important because it allows us to calculate the electric field for a given charge distribution. It also helps us understand the behavior of electric fields and how they are affected by the presence of charges.

4. Can Gauss's Law be applied to any charge distribution?

Yes, Gauss's Law can be applied to any charge distribution, as long as the charge is enclosed by the Gaussian surface. However, it is most useful for symmetric charge distributions, as it simplifies the calculation of the electric field.

5. How is Gauss's Law related to Maxwell's equations?

Gauss's Law is one of the four Maxwell's equations, which form the basis of classical electromagnetism. It is the first of the four equations and relates the electric field to the distribution of electric charges. The other three equations describe how electric and magnetic fields are related and how they are affected by changing electric and magnetic fields.

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