# Can charge really not be created?

The law of conservation of electric charge states that the net electric charge of an isolated system remains constant throughout any process.

In simple words, charge can neither be created nor destroyed.

The question that popped into my head is that if I take out some electrons from a neutral body, it would become positively charged. So didn't I just create some charge contradicting the law of conservation?

This feels kinda vacuous but what am I missing here?

• Note the law of conservation of electric charge does not say that charge cannot be created nor destroyed. It says that one cannot created or destroy any net charge on the system. You can create or destroy as much negative charge as you want so long as you create or destroy an equal amount of positive charge – Jim Aug 1 '17 at 11:43
• Similarly, neither conservation of energy nor conservation of momentum prevent you from pushing an object to give it energy and momentum, because the total energy and total momentum of the you-object-ground system are unaffected. – user2357112 Aug 1 '17 at 17:44
• Your first sentence assumed an "isolated system". Then you went and violated that assumption by removing the electrons. – Nacht Aug 1 '17 at 23:28
• "if I take out some electrons from a neutral body, it would become positively charged" You just used energy in order to create energy. – bitcell Aug 2 '17 at 9:36

if I take out some electrons from a neutral body, it would become positively charged. So didn't I just create some charge

You didn't create anything.

The electrons were already there (and so were the protons that make up the positive charge).

All you did was move them.

When you talk about conservation laws you have to include the whole system. If you're removing something from something else, you and what you remove are all part of the system to be considered.

EDIT :

A comment by @luk32 suggests mentioning a situation which can arise in particle physics where e.g. a neutral particle can decay into charged particles. Note that we again consider the complete system and when we include the new charged particles we find that they have a net charge of zero.

Many more complex conversions are possible in the quantum world, but again electric charge must be conserved and we have to pay careful attention to the what is include in the complete system to balance our sums.

An example of such an event might be the decay of the neutron.

• I think it's worth of mentioning it is possible to even create charges and not break conservation laws. The total charge of a system must remain the same. So while you can't create charge, you can actually create a charge given that it has appropriate pair. A reader should be cautious of the difference between particle and the quantity described by the same noun. – luk32 Aug 1 '17 at 11:27
• @luk32: But have you created charge, or just separated two tightly bound charges that made up the original particle? – jamesqf Aug 1 '17 at 18:20
• @jamesqf, they can be created and destroyed as long as total charge is conserved. Examine a electron-positron annihilation reaction. – BowlOfRed Aug 1 '17 at 18:25
• Just out of curiosity, say a virtual electron-positron pair is created from the vacuum; one of the pair falls into black hole and the other stays outside the black hole as a now "real" particle. It seems like in this case charge is conserved in the entire universe, but has the net charge of the "accessible" universe (i.e., outside the black hole) changed? – eipi10 Aug 1 '17 at 21:21
• @eipi10 Black holes "exhibit" only a few properties to the "outside" universe, and one of them is charge. This relates to a thing called the no hair theorem. So the sums still work. – StephenG Aug 1 '17 at 21:31

According to this formulation of the principle, you have just considered a system which is not isolated at all. Indeed a physical system is said isolated if it can exchange neither matter nor energy with the rest of the "universe".

Taking out some electrons from a volume of matter is equivalent to an interaction between two different systems: the one which is drawing negative charge and the other which is losing it. The right way of applying the charge conservation is to consider the (isolated) system made by the union of the previous two, which actually conserves a net zero charge.

Taking out electrons from a neutral body is analogous to saying $$0=1-1$$
You can write $0$ as the sum of $1$ and $-1$ but the $0$ doesn't go anywhere, it is still there. If you took some $-q$ charge out from the body, you also left behind $q$ charge on the body. So the net charge is still $0$.

Laws of conservation only require respective quantities to remain constant in closed systems or isolated systems (depending on the law in question). You can't take out electrons from a closed system, so either your system isn't closed (so the conservation law doesn't require the charge to remain constant), or your electrons are still there and the total charge didn't change.

• You are confusing "conservation" and "constancy" in isolated systems. Conservation of charge is always true because it includes the possible flow of charge. If the system is truly isolated (no current), then conservation leads to constancy. Removing electrons from the system constitutes a current, and conservation of charge is still true. – Bill N Aug 1 '17 at 15:45
• @BillN As I understand, any law of conservation of X can be formulated either for a closed system as $X = const$ or for an open system as $X_{t1} = X_{t2} + X_{in} - X_{out}$. I've never heard such laws being called "laws of constancy". – Dmitry Grigoryev Aug 1 '17 at 15:54
• I never said there was a law of constancy. I'm simply saying that charge conservation always happens, even if the amount charge within a small system changes. That's because the current is part of the conservation law. We should never say "charge isn't conserved in this system." – Bill N Aug 1 '17 at 17:58

## protected by Qmechanic♦Aug 1 '17 at 12:00

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