What is the mass difference between two charged objects with opposite charges?

[pinky2468]

I need some serious help! Unfortunately, my teacher this semester does not think that he should teach is, but that we should just learn it ourselves!
So, this is a very simple problem, but since I have no direction, I don't know where to start:

Object A is metallic and electrically neutral. It is carged by induction so it acquires a charge of -3.0x10^-6 C. Object B is identical to Object A and is also electrically neutral. It is charged by induction so that it acquires a charge of +3.0x10^-6 C. Find the difference in mass between the charged objects and state which has the greater mass.

Any help?

 

[maverick280857]

When you are charging a body you can do so either by contact or distance induction. In case of distance induction, charges are merely rearranged over the surface of the body as induction gives rise to a temporary electric field which causes charges to be isolated (initially charge on the body = 0, so it must be at any stage).

However, if charging takes place by actual contact, electron transfer takes place (there is nothing as positive charge in the classical model--a deficiency of electrons gives rise to a positive charge). Each electron has a rest mass of 9.31*10^(-31) kg (approximately) and if you know the number of electrons transferred then you know the mass change. (Here charge conservation may be applied only if you take the charged body and the charging body as a composite system.)

The key idea for the last step is to understand charge quantization: the idea simply means that any charge in the universe must be an integer multiple of the so called fundamental charge e (of the electron = 1.6*10^(-19)C).

Does that help?

Cheers
Vivek

 

[pinky2468]

It does help, but I am still not sure how to proceed. How do I figure out how many electrons have been transfered? There are no examples in my book and all I know is that q=Ne...N=q/e?

 

[Doc Al]

...all I know is that q=Ne...N=q/e?

Right. Use N = q/e (where q is the total charge and e is the charge per electron) to find the number of electrons that the object must have gained (or lost) to have a certain net charge. Then find the mass of that number of electrons. Vivek gave you all the constants that you need.

 

[pinky2468]

Would the net charge be 0? Then do I take the net charge and divide it by -1.6x10^-19?

 

[Doc Al]

Would the net charge be 0?

No. The net charge on each object, which is given.

Then do I take the net charge and divide it by -1.6x10^-19?

Yes.

 

[pinky2468]

I know this is an easy problem, but I am still confused about how to do it! If anyone can give me some more guidance on this...I can't finish my homework b/c I don't even know how to do the easy problems!

 

[Doc Al]

Start by finding the number of electrons transferred. We discussed how to do that in the last few posts.

 

[pinky2468]

Ok , so if I use N=q/e I get Na=-1.9x10^13 and Nb= +1.9x10^13? Is that right?

 

[Doc Al]

Right. One object gains that many electrons; the other loses that many. (Which is which?)

 

[pinky2468]

Object A gains -1.9x10^13 and Object B loses +1.9x10^13? If that is right, would the next step be to multiply by mass of e-

 

[Doc Al]

Object A gains -1.9x10^13 and Object B loses +1.9x10^13?

I would say it this way: The object with the negative charge gained 1.9x10^13 electrons while the one with the positive charge lost that same number of electrons.

If that is right, would the next step be to multiply by mass of e-

Yes. You need to figure out the total mass of 1.9x10^13 electrons. One object gains that much mass, the other loses that much mass. (Then you have to find the difference in mass of the two objects.)

 

[pinky2468]

So if I multiply them by 9.11x10^-31, I get 1.7x10^-17 But, I must be missing something b/c wouldn't the difference be zero? Do I add and subtract 9.11x10^-31 to 1.7x10^-17, the answer doesn't change

 

[Doc Al]

So if I multiply them by 9.11x10^-31, I get 1.7x10^-17 But, I must be missing something b/c wouldn't the difference be zero? Do I add and subtract 9.11x10^-31 to 1.7x10^-17, the answer doesn't change

One object weighs more by 1.7x10^-17 Kg, the other less. So what's the difference between them?

Think of it this way: Imagine two bags each with the same number of marbles. Take a marble from one bag and put it in the other. What's the difference in the number of marbles in the bags now?

 

[pinky2468]

I see what you are saying. Is it 3.4x10^-17?

 

[Doc Al]

Right! But don't forget the units: 3.4x10^-17 Kg.