How does conservation of charge work?

[AceInfinity]

Example: A conducting sphere X that has an initial charge of +2.0 × 10^–8 C and an identical conducting sphere Y that has an initial charge of –3.0 × 10^–8 C are touched together. After they are separated, the charge on sphere X is?

Answer: (–5.0 × 10^–9 C)

And what I would have done is tried to balance them out by adding them together and dividing by 2, but either way I can't understand how they got an exponent of "-9"

Not a homework problem, I just need to understand what's going on here, and how to come up with solutions to solving this type of problem with charged particles.

 

[vkash]

Example: A conducting sphere X that has an initial charge of +2.0 × 10^–8 C and an identical conducting sphere Y that has an initial charge of –3.0 × 10^–8 C are touched together. After they are separated, the charge on sphere X is?

Answer: (–5.0 × 10–9 C)

And what I would have done is tried to balance them out by adding them together and dividing by 2, but either way I can't understand how they got an exponent of "-9"

Not a homework problem, I just need to understand what's going on here, and how to come up with solutions to solving this type of problem with charged particles.

AceInfinity is this complete question. if yes then answer(–5.0 × 10–9 C) may wrong. How charge distribution occur it depends on capacitance of that body. In your question you say identical conducting sphere so their capacitance equal so charge should equal on both sphere and you are seeming correct.

if capacitance of two sphere is different say C1 and C2 then we use the point that potential on both the sphere should equal(as they are in contact).V1=V2 => Q₁/c₁=q₂C₂ q and c represent their charge and capacitance respectively.
Hope my my answer helps.

 

[jtbell]

by adding them together

What number do you get at this point?

and dividing by 2

And what number do you get at this point?

 

[AceInfinity]

AceInfinity is this complete question. if yes then answer(–5.0 × 10–9 C) may wrong. How charge distribution occur it depends on capacitance of that body. In your question you say identical conducting sphere so their capacitance equal so charge should equal on both sphere and you are seeming correct.

if capacitance of two sphere is different say C1 and C2 then we use the point that potential on both the sphere should equal(as they are in contact).V1=V2 => Q₁/c₁=q₂C₂ q and c represent their charge and capacitance respectively.
Hope my my answer helps.

Not sure. I'm still convinced that the answer they gave in the answer key is correct because this is from a practice Diploma.

@jtbell I got 5.00x10⁸

Dividing that by 2 would equal 2.50x10⁸

I'm still confused though, as the way I was doing it must be wrong, so doing that is irrelevant. I was keeping to the numbers as if they were absolute values.

 

[Nabeshin]

Not sure. I'm still convinced that the answer they gave in the answer key is correct because this is from a practice Diploma.

@jtbell I got 5.00x10⁸

Dividing that by 2 would equal 2.50x10⁸

I'm still confused though, as the way I was doing it must be wrong, so doing that is irrelevant. I was keeping to the numbers as if they were absolute values.

Ah yes! Remember that there exist both positive and negative charges, so the sign associated with the charge is very important!

 

[AceInfinity]

I know, There's just that number of charges MORE as those numbers are only net charges, but how would you solve this? Still doesn't answer that

 

[Born2bwire]

They are identical spheres and we can assume symmetry at work in this problem. So we know that after touching and drawing them apart that they should have the same net charge. We know this because a conductor is an equipotential surface and so when they are brought in contact the amalgamation of the two spheres becomes a single equipotential surface. Thus, the charge becomes evenly distribtuted across the two spheres when they come in contact (via symmetry and equipotential).

Next, how much charge is there? When you bring the two spheres together, what is the net charge that is distributed across the surfaces? Now when you separate the spheres, what is the net charge distributed on each sphere? As Nabeshin stated, you need to remember to keep track of the sign.

 

[cjl]

I know, There's just that number of charges MORE as those numbers are only net charges, but how would you solve this? Still doesn't answer that

Nabeshin gave you a big hint. Signs are critical to this problem.

(You aren't adding correctly)

 

[AceInfinity]

Alright, so I added them as If they weren't absolute values and ended up with the smaller number (exponent -9) I should have assumed that was the case since there's no other way that I would end up with a smaller number than to end up with a smaller number through the adding process, and the only way to do that would to be to minus the 3. (Which would also give me a "-"5 result...)

Guess I just wasn't thinking:

[(+2.0 × 10^-8) + (-3.0 x 10^-8)] ÷ 2 = -5.0x10^-9