How do we know that both plates of a capacitor have the same charge?

In summary, when two conductors of different shapes are connected to a battery, equal amounts of charge will appear on each conductor. This is due to the principle of charge conservation, which states that if the total charge on a system is zero, then the positively charged components must have equal and opposite charge in total to the negatively charged components. The initial net charge in the system can vary, and charge cannot be created or destroyed. However, charge conservation does not necessarily imply equal amounts of charges on the two plates of a capacitor in a particular set-up. Understanding how a battery works is important, as demonstrated by Heisenberg's near-failure on his PhD examination due to his lack of knowledge on the topic.
  • #1
Kashmir
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Suppose we have two conductors ( can be of different shapes) and connect them to battery.
Why would equal amounts of charge appear on the two conductors?
 
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  • #2
What was the initial net charge in the system? Can charge be created or destroyed?
 
  • #3
Kashmir said:
Suppose we have two conductors ( can be of different shapes) and connect them to battery.
Why would equal amounts of charge appear on the two conductors?
Do you have a particular set-up in mind? In general, if the total charge on a system is zero, then the positively charged components must have equal and opposite charge in total to the negatively charged components.
 
  • #4
Ibix said:
What was the initial net charge in the system? Can charge be created or destroyed?
Maybe the two plates of capacitor have unequal charges. The excess goes to battery somehow.
 
  • #5
PeroK said:
Do you have a particular set-up in mind? In general, if the total charge on a system is zero, then the positively charged components must have equal and opposite charge in total to the negatively charged components.
Yes that should be true for the whole system. Battery, wires and plates of capacitor.

Charge conservation doesn't necessarily imply equal amounts of charges on the two plates of capacitor.
 
  • #6
Kashmir said:
Yes that should be true for the whole system. Battery, wires and plates of capacitor.

Charge conservation doesn't necessarily imply equal amounts of charges on the two plates of capacitor.
IMO, you asked the wrong question. Your question should have been: how does a battery work?

In fact, Heisenberg nearly failed his PhD examination because he didn't know how a storage battery worked!
 
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  • #8
They don't have to be precisely equal. However if they are not, that means there is an overall charge. In electrical terms, that overall charge is on the self-capacitance of the capacitor. Let's put some numbers on it.
Take a 100uF capacitor. Place 1,000 microcoulombs on one plate and -1,000 on the other. The capacitor is then charged to 10v and there is no left-over charge. But now add a further charge of 1 nanocoulomb to one plate. That's one part in a million imbalance. A typical small capacitor might have a self-capacitance of 1 pF. The nanocoulomb raises its potential by 1000 volts - 100 times the plate-to-plate voltage.
You also have what are usually called "stray" capacitances, such as from the body of the capacitor to adjacent conductors, be they "earth/ground" or something else. These may very well be a bit larger than the self capacitance but if we say 10pF, that still leaves the one part per million imbalance raising the overall potential by 100 volts.

So there is no absolute law saying the charges are the same. However if they are not, there will be huge voltages trying to get the imbalance away. Besides which, you are most unlikely to want to operate a capacitor like that.

No, you can't just get rid of a charge "into the battery". Sometimes garage mechanics don't use scientific terms very accurately. To a mechanic, putting charge into a battery means sending a current through it. So the charge that goes in is equal to the charge that comes out. A battery doesn't just magically absorb charge.
 
  • #9

FAQ: How do we know that both plates of a capacitor have the same charge?

How do we know that both plates of a capacitor have the same charge?

We know that both plates of a capacitor have the same charge because of the principle of charge conservation. When a capacitor is charged, electrons are transferred from one plate to the other, creating an equal but opposite charge on each plate. This ensures that the net charge of the system remains zero.

What role does the dielectric material play in ensuring equal charge on the capacitor plates?

The dielectric material in a capacitor does not directly ensure that both plates have equal charge. Instead, it increases the capacitor's ability to store charge by reducing the electric field between the plates, allowing for a higher charge to be stored at a given voltage. The equal and opposite charges on the plates are due to the conservation of charge during the charging process.

Can external influences affect the charge equality on the capacitor plates?

External influences such as nearby electric fields or physical disturbances can temporarily affect the distribution of charges on the capacitor plates. However, under normal operating conditions and in a closed system, the charges on the plates will remain equal and opposite due to the conservation of charge.

How does connecting a capacitor to a voltage source ensure equal and opposite charges on the plates?

When a capacitor is connected to a voltage source, electrons are pushed from the negative terminal of the source to one plate of the capacitor and pulled from the other plate to the positive terminal. This movement of electrons results in one plate gaining a negative charge and the other plate gaining an equal positive charge, ensuring that the charges are equal in magnitude but opposite in sign.

Is it possible for a capacitor to have unequal charges on its plates under any circumstances?

Under ideal conditions, a capacitor will always have equal and opposite charges on its plates. However, in practical scenarios, factors such as leakage currents, imperfections in the dielectric material, or physical damage to the capacitor can cause slight imbalances. These imbalances are typically very small and do not significantly affect the overall behavior of the capacitor.

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