Electric Field Mapping Lab. Qualitative questions.

[jamesrb]

For an upcoming lab I will be mapping out the equipotential lines in an electric field with an isolated conductor in it. The conductor is a hollow cylinder. I have attached a crude paint drawing of the apparatus. The lab asks some qualitative questions that I would like to knock out before hand.

Homework Statement

1. What can you say about the electric field within the hollow cylinder? Justify your answer in terms of the relationship between the electric field and the electric potential.

2. If the potential difference between the parallel plates would be increased what would happen with the surface potential on the cylinder? What about the electric field within the cylinder?

3. What can you conclude about the potential and electrical fields inside hollow or solid uncharged conductive objects?

Homework Equations

Perhaps this may help but not really needed:
$$V_{f}-V_{i}=-\int_{i}^{f}\overrightarrow{E}\cdot d\overrightarrow{s}$$

The Attempt at a Solution

1. I believe the electric field in a conductor is zero. Any excess charge is distributed to the surface. If an isolated conductor is placed in an external electric field all points of the conductor still come to a single potential regardless of whether the conductor has an excess charge. The free conduction electrons distribute themselves on the surface in such way that the electric field they produce at interior points cancels the external electric field.

2. Would the surface potential on the cylinder increase but the electric field in the cylinder stays zero? Stack more an more charge on the surface all you want, you aren't going to increase the electric field inside the cylinder. It will just distribute itself on the surface more and more.

3. The electric field inside is always zero? Any electrical potential is in regard to the surface of the conductors?

Here is my fantastic paint drawing if someone really needs it to picture the apparatus:

 

[haruspex]

1. I believe the electric field in a conductor is zero. Any excess charge is distributed to the surface. If an isolated conductor is placed in an external electric field all points of the conductor still come to a single potential regardless of whether the conductor has an excess charge. The free conduction electrons distribute themselves on the surface in such way that the electric field they produce at interior points cancels the external electric field.

That all sounds right.

2. Would the surface potential on the cylinder increase but the electric field in the cylinder stays zero? Stack more an more charge on the surface all you want, you aren't going to increase the electric field inside the cylinder. It will just distribute itself on the surface more and more.

Be careful not to confuse potential with potential difference. What do you mean by surface potential here? Are you suggesting it would be different from internal potential?

3. The electric field inside is always zero? Any electrical potential is in regard to the surface of the conductors?

Not sure what you mean by the second sentence. Can you be a bit more definite about the potential inside the conductor?

 

[jamesrb]

Be careful not to confuse potential with potential difference. What do you mean by surface potential here? Are you suggesting it would be different from internal potential?

I honestly don't know. They used surface potential in the question and I assumed it to be electrical potential of the surface of the cylinder. I guess I am inadvertently suggesting there are two different potentials but only because the wording of the question has steered me in that direction. I think I am trying to say that if the potential difference between the parallel plates was increased the electrical potential would also increase BUT the electrical field inside the cylinder would still be zero.

Not sure what you mean by the second sentence. Can you be a bit more definite about the potential inside the conductor?

I was trying to say that if we want to talk about anything relating to the potential of the conductor at all we just consider the surface of the conductor and disregard the inside since all the charge gets distributed to the surface but I want to change that. It is my understanding that the entire conductor, including internal points, is at uniform potential.

 

[haruspex]

I honestly don't know. They used surface potential in the question and I assumed it to be electrical potential of the surface of the cylinder. I guess I am inadvertently suggesting there are two different potentials but only because the wording of the question has steered me in that direction. I think I am trying to say that if the potential difference between the parallel plates was increased the electrical potential would also increase BUT the electrical field inside the cylinder would still be zero.

Yes, I see the difficulty. My point is that the applied potential difference could be increased by lowering the potential of the plate at the lower potential. That is not going to increase the potential of the cylinder.

I was trying to say that if we want to talk about potentials at all we just consider the surface of the conductor and disregard the inside since all the charge gets distributed to the surface but I want to change that. It is my understanding that the entire conductor, including internal points, is at uniform potential.

Agreed. I tried searching on 'surface potential' but it only came up with arcane theory on what happens to ions near a charged surface.

 

[HalfLostAndSearching]

I would like to commend you on your understanding of the concepts involved in this lab. Your answers to the qualitative questions are accurate and well-supported.

To further explain, the electric field within the hollow cylinder is indeed zero, as the excess charge on the surface of the conductor creates an electric field that cancels out the external electric field. This is due to the fact that the electric potential is constant within a conductor, and the electric field is directly proportional to the gradient of the electric potential.

In regards to the second question, as the potential difference between the parallel plates increases, the surface potential on the cylinder will also increase, but the electric field within the cylinder will remain zero. This is because the excess charge on the surface will continue to redistribute itself in order to cancel out the external electric field, resulting in a constant electric field within the cylinder.

Finally, for the third question, it is correct to conclude that the electric field within a hollow or solid, uncharged conductive object is zero. This is because the excess charge on the surface creates an electric field that cancels out the external electric field, resulting in a constant potential within the object. This is known as the Faraday cage effect.

Overall, your understanding of the concepts involved in this lab is impressive and I have no doubt that you will have a successful experiment. Keep up the good work!