Does This Van de Graaff Generator Question Make Sense?

[daNAV1GATOR]

I would just like someone to please read this question below and tell me if it makes any sense. [This question is in my exam]


(I've already solved this problem -- but the next question is a continuation)
So the FIRST QUESTION (which I've solved):
If a Van de Graaff generator is charged to 50,000 volts, how much energy does it take to add an additional electron to the charge on the sphere?
*my answer: 8.0 x 10^-15 joules*


NOW THE SECOND QUESTION is the one I don't understand.
How would the voltage of the generator in Part (A) compare to the voltage of a larger Van de Graaff generator with the same amount of charge? To which generator could an electron be added with the least expenditure of energy?


..."How would the voltage.. [50,000V] ..compare to the generator of a larger VdG generator WITH THE SAME AMOUNT OF CHARGE?"
---what does that mean?---

I know that the larger generator can be charged to a higher voltage...
is that the answer??


Thanks in advance!

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Doc Al]

..."How would the voltage.. [50,000V] ..compare to the generator of a larger VdG generator WITH THE SAME AMOUNT OF CHARGE?"
---what does that mean?---

The charge is kept the same on both generators. You know the voltage needed to charge the small one; how does that voltage compare with the voltage needed to charge the larger one to the same charge?

 

[daNAV1GATOR]

"How does that voltage compare with the voltage needed to charge the larger one to the same charge?"So... the answer to that would be -- A higher voltage is needed to charge the larger generator to the same charge. -?

 

[Doc Al]

So... the answer to that would be -- A higher voltage is needed to charge the larger generator to the same charge. -?

What's your reasoning? How did you conclude that? What determines the potential of a charged sphere?

 

[daNAV1GATOR]

man... this is hard...

let me think about it. =)

 

[Doc Al]

Here's a hint to get you thinking. Is it harder to charge a small sphere or a large sphere with the same amount of charge. Why?

 

[daNAV1GATOR]

*sigh*

i'm really having a hard time here... don't know where to start! hehe =)
(I'm homeschooled and so I don't have a Physics teacher)

So about "the same amount of charge" ... does that mean 50,000 volts? But volts is not a measure of charge, correct? Coloumb is the unit of charge!

And about charging a sphere.. a sphere becomes negatively charged when there are more electrons than protons, correct?

 

[daNAV1GATOR]

someone please share their thoughts?

Doc Al?

 

[Doc Al]

Think of building the charge on the sphere by adding electrons. Since the electrons repel each other more strongly as they are forced closer together, which would it be harder to put the same negative charge on: a small sphere or a larger sphere?

Read up on the potential of a charged sphere: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potsph.html"

 

[Doc Al]

If a Van de Graaff generator is charged to 50,000 volts, how much energy does it take to add an additional electron to the charge on the sphere?

Just an FYI: Van de Graff generators are typically positively charged. You build up a positive charge by removing electrons. (I suspect it's a typo in your question.)

 

[daNAV1GATOR]

...It would be harder to add electrons to a small sphere than a large one with the same amount of charge simply because there is less space in the small sphere.

 

[daNAV1GATOR]

'OlderDan' also made a comment about the charge of the generator [in 2005]

https://www.physicsforums.com/showthread.php?t=79131

 

[Doc Al]

...It would be harder to add electrons to a small sphere than a large one with the same amount of charge simply because there is less space in the small sphere.

It's harder to add electrons to a smaller sphere because you'd need to force them closer together (not because there's less space). They resist being brought closer, so you need a greater voltage to charge the smaller sphere to the same charge compared to a larger sphere.

 

[Doc Al]

'OlderDan' also made a comment about the charge of the generator [in 2005]

Yep. Same problem. (Same error!)

What book are you using?

 

[daNAV1GATOR]

Okay... so now going back to the original question... How would the voltage compare?

"The voltage required for the larger generator to have the same amount of charge is less than 50,000 volts because the electrons in the larger sphere would not be as compressed as in the smaller sphere."

--sound good? =) So electrons in a sphere are basically the same as air in a balloon?

the second question in the same problem... To which generator could an electron be added with the least expenditure of energy?

answer: "Adding an electron to the larger generator would take less energy."

 

[daNAV1GATOR]

Doc Al:
"Yep. Same problem. (Same error!)
What book are you using?"

REPLY:

What do you mean same error?
Should the 8.0 x 10^-15 C be positive or negative?
At first I kept it positive... But then I changed it to Negative because the question adds: "The charge on an electron is given in Question 26 above." So with that info, I decided to make in Negative because the charge shown in the question above is -1.6 x 10^-19 C.I'm enrolled in American School (correspondence school)
and the Physics book they gave me is the Conceptual Physics by Paul G. Hewitt.
It's a great book overall...

 

[daNAV1GATOR]

Doc Al! you're back Online!

please check my answer.
thanks!

 

[Doc Al]

Okay... so now going back to the original question... How would the voltage compare?

"The voltage required for the larger generator to have the same amount of charge is less than 50,000 volts because the electrons in the larger sphere would not be as compressed as in the smaller sphere."

OK.

--sound good? =) So electrons in a sphere are basically the same as air in a balloon?

The extra charge on a conductor is entirely on the surface of the conductor, not inside the sphere. Picture the charges as ants on a ball. The same number of ants on a smaller ball are crowded closer together.

the second question in the same problem... To which generator could an electron be added with the least expenditure of energy?

answer: "Adding an electron to the larger generator would take less energy."

OK.

Doc Al:
"Yep. Same problem. (Same error!)
What book are you using?"

REPLY:

What do you mean same error?
Should the 8.0 x 10^-15 C be positive or negative?
At first I kept it positive... But then I changed it to Negative because the question adds: "The charge on an electron is given in Question 26 above." So with that info, I decided to make in Negative because the charge shown in the question above is -1.6 x 10^-19 C.

The problem with the problem statement is this. Van de Graff generators are positively charged, not negatively charged. If it were negatively charged, the voltage would have to be negative.

Did you copy the problem word for word, exactly as given in the book?

I'm enrolled in American School (correspondence school)
and the Physics book they gave me is the Conceptual Physics by Paul G. Hewitt.
It's a great book overall...

That's a good book. While I don't have it handy, I did use it for a course I taught many years ago. So I'm familiar with his style.

 

[daNAV1GATOR]

Thanks a lot!

pretty behind in my HighSchool... I need to finish this year.
argh!

================

Yes, I copied the problem word for word.

Thanks again!

but I might need some help again in the future... haha