Does This Van de Graaff Generator Question Make Sense?

  • Thread starter Thread starter daNAV1GATOR
  • Start date Start date
Click For Summary
SUMMARY

The discussion revolves around the physics of Van de Graaff generators, specifically addressing the energy required to add an electron to a charged sphere and the comparison of voltages between a smaller and a larger generator with the same charge. The user correctly calculated that adding an electron to a Van de Graaff generator charged to 50,000 volts requires 8.0 x 10^-15 joules of energy. It was concluded that a larger generator requires a lower voltage to achieve the same charge due to less electron compression, making it easier to add electrons to the larger generator.

PREREQUISITES
  • Understanding of electric potential and voltage
  • Knowledge of charge units, specifically Coulombs
  • Familiarity with the operation of Van de Graaff generators
  • Basic principles of electrostatics and electron behavior
NEXT STEPS
  • Research the relationship between charge and voltage in capacitors
  • Learn about the physics of charged spheres and their electric fields
  • Study the principles of electrostatic repulsion and attraction
  • Explore advanced topics in electrostatics, such as Gauss's Law
USEFUL FOR

Students studying physics, particularly those focusing on electrostatics, as well as educators and anyone interested in the practical applications of Van de Graaff generators in experiments.

daNAV1GATOR
Messages
45
Reaction score
0
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


 
Physics news on Phys.org
daNAV1GATOR said:
..."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?
 
"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. -?
 
daNAV1GATOR said:
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?
 
man... this is hard...

let me think about it. =)
 
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?
 
*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?
 
someone please share their thoughts?

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"
 
Last edited by a moderator:
  • #10
daNAV1GATOR said:
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.)
 
  • #11
...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.
 
  • #13
daNAV1GATOR said:
...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.
 
  • #14
daNAV1GATOR said:
'OlderDan' also made a comment about the charge of the generator [in 2005]
Yep. Same problem. (Same error!)

What book are you using?
 
  • #15
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."
 
  • #16
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...
 
  • #17
Doc Al! you're back Online!

please check my answer.
thanks!
 
  • #18
daNAV1GATOR said:
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.

daNAV1GATOR said:
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.
 
  • #19
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
 

Similar threads

Van de Graaff generator questions?
  • · Replies 12 ·
Replies
12
Views
7K
What is the Speed and Number of Protons in a Van de Graaff Generator Beam?
  • · Replies 3 ·
Replies
3
Views
4K
Van der Graaf Generator: Charge, Potential and Redesign Questions
  • · Replies 8 ·
Replies
8
Views
3K
How Does Proximity to a Van de Graaff Generator Affect an Insulated Conductor?
  • · Replies 1 ·
Replies
1
Views
1K
Van de Graaff generator? adding a electron?
  • · Replies 8 ·
Replies
8
Views
4K
How Can I Improve My DIY Van de Graaff Generator to Prevent Charge Leakage?
  • · Replies 5 ·
Replies
5
Views
2K
How to Calculate Force for Van de Graaff Generator | 70-Year Old Challenge
  • · Replies 7 ·
Replies
7
Views
4K
Simple Van de Graaff Generator Problem
  • · Replies 1 ·
Replies
1
Views
3K
High School Ground for a Van de Graaff Generator?
  • · Replies 3 ·
Replies
3
Views
3K
The force between charged and neutral object
  • · Replies 2 ·
Replies
2
Views
2K