Measuring Electrical Potential and Electrical Fields without a computer

[piareround]

Hey physics forums

I was kind of curious if there how people measured electric field and of course Gauss's law before we had computers, so I talked to one of my professors about it. He told me that a long time ago people used something involving plates and soap bubbles to prove that Gauss's law was valid.

Does anyone have a way of physically showing and measuring Gauss's law without the need for computer, diode sensors, or calculator? Has anyone heard of this soap bubble method before?

 

[BruceW]

There are many different forms of Gauss' Law. (for example in electric fields, or for gravitational fields).

I'm not sure about soap bubbles... They act to minimise their surface area, but I'm not sure what that has to do with Gauss' Law..

When Gauss made his law for the electric field, I reckon he was going partly by experimental evidence and partly by intuition. I find it incredible that the classical laws of electromagnetism are so simple in form.

EDIT: Also, the Divergence theorem has been mathematically proven, so this gives a link between Gauss' law for electric fields and Coulomb's law. (In other words, if we assume Coulomb's law is true, then Gauss' law must also be true).

 

[piareround]

Well I was talking to my professor and he e-mailed me this link a few minutes ago.

http://books.google.com/books?id=Pd...&resnum=4&ved=0CDMQ6AEwAw#v=onepage&q&f=false

Does anyone recognize what this book is talking about? Anything similar that could be used to make an experiment?

There are many different forms of Gauss' Law. (For example in electric fields, or for gravitational fields).

I'm not sure about soap bubbles... They act to minimize their surface area, but I'm not sure what that has to do with Gauss' Law..

When Gauss made his law for the electric field, I reckon he was going partly by experimental evidence and partly by intuition. I find it incredible that the classical laws of electromagnetism are so simple in form.

EDIT: Also, the Divergence theorem has been mathematically proven, so this gives a link between Gauss' law for electric fields and Coulomb's law. (In other words, if we assume Coulomb's law is true, then Gauss' law must also be true).

Correct. However, I feel like BruceW it stands to reason that, if we still use it 150 years later, Gauss’s original law from 1867 should have been subject to some-kind of scientific inquiry that did not involve computers or graphic models. The problem that I am finding as a lab teaching assistant is that there is not tactile or kinetic way of teaching Gauss’s Law. I have to show that it’s real beyond just the mathematical relationships like Divergence that link it to other theories. Students know how to calculate Gauss’s law and Electric field lines even to the point to create enclosed Gaussian surfaces when they are asked a pencil and paper problem. However, when you give them a physical object, they are completely lost and make the connection between what they did by paper and pencil to its applications in the real world. I am not sure if you have seen the same thing in other physics class rooms, but many of the student's in my class have trouble applying Gauss’s Law because they don't think it’s real or don't have a sense of how real it is.

Thus, I am looking for a pre-computer way of testing/measuring for Gauss’s law, so I can turn it into an actual physical demonstration of Gauss’s law.

 

[xts]

Students know how to calculate Gauss’s law and Electric field lines even to the point to create enclosed Gaussian surfaces when they are asked a pencil and paper problem. However, when you give them a physical object, they are completely lost and make the connection between what they did by paper and pencil to its applications in the real world.

It is much more general problem Gauss law is nothing exceptional among other laws - students (majority) are lost always if they must apply physics to real world. The way how they are taught in schools is so abstract, that they are unable to find relations between physical laws and reality. Do you remember Feynman's story about Brasilian students and polarisation of light reflected from water surface?
In some countries it is a bit better, in some a bit worse, but all over the world educational problem is the same: kids are taught to memorize formulae, then apply them to "realistic" scenarios of school excercises, which often contradict common experience.
So they learn: physics apply to excercises, the real world is ruled by common sense experience, those two have little (if any) in common.

 

[BruceW]

Correct. However, I feel like BruceW it stands to reason that, if we still use it 150 years later, Gauss’s original law from 1867 should have been subject to some-kind of scientific inquiry that did not involve computers or graphic models. The problem that I am finding as a lab teaching assistant is that there is not tactile or kinetic way of teaching Gauss’s Law. I have to show that it’s real beyond just the mathematical relationships like Divergence that link it to other theories. Students know how to calculate Gauss’s law and Electric field lines even to the point to create enclosed Gaussian surfaces when they are asked a pencil and paper problem. However, when you give them a physical object, they are completely lost and make the connection between what they did by paper and pencil to its applications in the real world. I am not sure if you have seen the same thing in other physics class rooms, but many of the student's in my class have trouble applying Gauss’s Law because they don't think it’s real or don't have a sense of how real it is.

Thus, I am looking for a pre-computer way of testing/measuring for Gauss’s law, so I can turn it into an actual physical demonstration of Gauss’s law.

Good point here. Although I don't know how computers have made it easier to explain Gauss' law.

One way to explain Gauss' law for electric fields is to simply say that it is mathematically similar to Coulomb's law. But as you said, you need to explain it more than just as an abstract mathematical theory.

If I was explaining Gauss' law for electric fields without using Coulomb's law, i would say:
"Gauss' law tells us that electric charges act as a source (or sink) of the electric field. Therefore, the electric flux out of a closed volume depends on the charges enclosed."

What problems do the students have in applying Gauss' law to real objects? I guess Gauss' law is only easy when there is high symmetry involved. And conversely, Coulomb's law can be imagined even when there isn't a symmetry (since you just imagine each small charge making its own electric field, all of which add up).

I think maybe Gauss' law is simply less intuitive than Coulomb's law. And if I think of some commonly shaped charge distributions, the electric field outside those charges is usually much easier to calculate using Coulomb's law and summing over all charges. (Unless the charge distribution is spherically symmetric, in which case Gauss' law is easier).

 

[xts]

I agree with BruceW that the best way to teach Gauss law is to derive it from Coulomb's law, and make labs/demos for the last.

There are some "classic" school demonstrations showing:
- the electric field of the charged sphere do not depend on its radius, only on its charge,
- the potential of charged sphere is reverse proportional to its radius if the charge is constant,
- the charge is proportional to the radius if potential is constant.