# Electric Field Mapping Lab. Qualitative questions.

1. Feb 1, 2014

### 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.

1. The problem statement, all variables and given/known data
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?

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

3. 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:

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Feb 1, 2014

### haruspex

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

3. Feb 1, 2014

### jamesrb

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.

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.

Last edited: Feb 1, 2014
4. Feb 1, 2014

### haruspex

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