# How does conservation of charge work?

• AceInfinity
In summary: Thanks for the help!In summary, the solution to this problem involves keeping track of the signs of the charges and using the concept of equipotential surfaces to determine the distribution of charge on the two identical conducting spheres. By bringing the spheres in contact, the net charge becomes evenly distributed across both spheres. After they are separated, the net charge on each sphere is equal, with one sphere having a positive charge and the other having a negative charge. By remembering to include the signs in the calculations, we can determine the correct answer of (–5.0 × 10–9 C) for the charge on sphere X.
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.

Last edited:
AceInfinity said:
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.

AceInfinity said:
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?

vkash said:
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.

AceInfinity said:
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!

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

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.

AceInfinity said:
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)

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

## 1. How does conservation of charge work?

The law of conservation of charge states that electric charge cannot be created or destroyed, it can only be transferred from one object to another. This means that the total amount of charge in a closed system remains constant.

## 2. What is the significance of conservation of charge?

Conservation of charge is a fundamental law of physics that helps explain the behavior of electric charges. It allows us to predict and understand how electric charges interact with each other, and is the basis for many important concepts in electromagnetism.

## 3. How does conservation of charge apply to everyday life?

Conservation of charge is present in many everyday phenomena, such as when you rub a balloon on your hair and it sticks to a wall. This is due to the transfer of electrons from your hair to the balloon, causing an imbalance of charges and creating a temporary electric field.

## 4. Can conservation of charge be violated?

No, conservation of charge is considered a fundamental law of nature and has been extensively tested and proven through various experiments. Any apparent violations of this law can be explained by the transfer of charge from one object to another.

## 5. How does conservation of charge relate to other conservation laws?

Conservation of charge is closely related to other conservation laws, such as conservation of energy and conservation of momentum. These laws all stem from the principle of conservation, which states that certain properties of a closed system cannot change over time.

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