Van de Graaff generator? adding a electron?

[graphicer89]

Van de Graaff generator? adding a electron??

Homework Statement

A)If a Van de Graaff generator is charged to 5,000 volts, how much energy does it take to add and additional electron to the charge on the sphere? If the charge of an electron is -1.6 x 10 ^-19...

B) How would the voltage of the generator in the 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 addded with the least expenditure of energy?

Homework Equations

Are there any equations i can apply?

The Attempt at a Solution

A) I guessed but i don't know if I am right or wrong...i multiplied...

5,000 v x -1.6 x10^-19 C = -8 x 10^-16 energy but i think that's wrong can you please help me with the calculations? i don't know to multiply or divide...


B) I need to do A first to understand B...but my guess is that the voltage is the same but the force or work to include a electron would not be much in a larger generator. Its easier to add a electron to a larger Van de Graaff generator with the least expenditure of energy...

 

[diazona]

A) I guessed but i don't know if I am right or wrong...i multiplied...

5,000 v x -1.6 x10^-19 C = -8 x 10^-16 energy but i think that's wrong can you please help me with the calculations? i don't know to multiply or divide...

-8 x 10^-16 Joules. Joules are the units of energy. If you'd written that, it would be correct. (You used the formula U = qV)

B) I need to do A first to understand B...but my guess is that the voltage is the same but the force or work to include a electron would not be much in a larger generator. Its easier to add a electron to a larger Van de Graaff generator with the least expenditure of energy...

If the voltage were the same, the work required would be the same. But the voltage is not the same. Here's a hint: what do you know about capacitance?

 

[graphicer89]

-8 x 10^-16 Joules. Joules are the units of energy. If you'd written that, it would be correct. (You used the formula U = qV)


If the voltage were the same, the work required would be the same. But the voltage is not the same. Here's a hint: what do you know about capacitance?

Honestly nothing...but this is kinda like earth..earth is so large that it consumes an infinite amount of energy and it never over flows..etc...so I am thinking...would it require more energy to add a electron to a small generator because its more compact?...i really don't want to go off topic...

 

[diazona]

Honestly nothing...but this is kinda like earth..earth is so large that it consumes an infinite amount of energy and it never over flows..etc...so I am thinking...would it require more energy to add a electron to a small generator?

Not actually an infinite amount of energy, more like so-large-that-for-most-cases-it-might-as-well-be-infinite. But anyway: yes it would require more energy to add an electron to a small generator, now can you figure out why? Go back to your references (textbooks, notes, whatever you have) and look up some information on capacitance if you need to.

 

[graphicer89]

Not actually an infinite amount of energy, more like so-large-that-for-most-cases-it-might-as-well-be-infinite. But anyway: yes it would require more energy to add an electron to a small generator, now can you figure out why? Go back to your references (textbooks, notes, whatever you have) and look up some information on capacitance if you need to.

This is what i found...

The electrical potential energy of a charged particle is increased when work is done to push it against the electric field of something else that is charged. Just as work is done to compress a spring work is done in pushing the charge against the electric field of the sphere. This work is eqqual to the energy gained by the charge.

 

[diazona]

OK, that's true, but surely there must be more than that? (You don't need to post it here, but you should read it yourself!) Especially keep your eyes open for a formula involving voltage that has to do with capacitance.

 

[graphicer89]

OK, that's true, but surely there must be more than that? (You don't need to post it here, but you should read it yourself!) Especially keep your eyes open for a formula involving voltage that has to do with capacitance.

well actually what i tried looking but i just feel like I am in a dead end right now

 

[graphicer89]

So there's more voltage in the first sphere than in the second...

 

[graphicer89]

Nevermind I figured it out thanks though fr your help