Charge reconfiguration on wires connnected to capacitor

[Jyothish]

Consider a capacitor which is charged to a certain voltage 'V' and having a total charge 'q' in it.The leads of the capacitor are connected to ideal conducting wire strips.Now if I introduce one conductor slab between plates of the capacitor, without touching the plates,as we know from basic electrostatics that the resultant capacitance increases.This means that ,for the same charge, potential difference between plates of the capacitor is reduced.This is easily explainable if we consider the the electric field 'E' between plates and integrate it between plate separation.

However, please consider the following
1) Since the wire strips are connected to plates, each wire strip will have the same potential as that of plate to which it is connected

2)Potential difference between plates must be equal to the potential difference between wire strips

3)Potential difference is independent of path.Hence if we integrate the electric field 'E' between the wire strips, by following a path without going through the capacitor, I should get the same potential difference.

But ,when we introduce the conductor slab, to get a reduced potential difference(by integrating ' E' without going through capacitor) between wire strips, the surface charge configuration of wire strips must be altered.In this case surface charges should be reduced,I guess

I am not getting, which mechanism does this re-configuration of charges.And also, where is the excess charge going to

If my assumption that the surface charge on the wires are reduced is incorrect,how we will get a reduced potential difference when 'E' is integrated over a path(not through capacitor) between wire strips.

 

[mfb]

But ,when we introduce the conductor slab, to get a reduced potential difference(by integrating ' E' without going through capacitor) between wire strips, the surface charge configuration of wire strips must be altered.In this case surface charges should be reduced,I guess

Right. This is completely negligible for most realistic setups. The capacitor plates will get a tiny increase in surface charges and electric field strength.

You can model this system with two capacitors in parallel, where you increase the capacitance of the significantly larger one.

 

[Jyothish]

thank you for the reply

 

[Svein]

Now if I introduce one conductor slab between plates of the capacitor, without touching the plates

What you do is equivalent to changing the circuit to having two capacitors in series, with the same resulting capacitance as the original capacitor. I cannot quite see what difference it should make to the rest of the circuit.

 

[alphy]

I would first like to clarify that the concept of charge reconfiguration on wires connected to a capacitor is a complex one and requires a deep understanding of electrostatics and circuit theory. However, I will try my best to provide a response to the content provided.

Firstly, when a conductor slab is introduced between the plates of a charged capacitor, the capacitance of the system increases. This is because the electric field between the plates is reduced due to the presence of the conductor slab, resulting in a decrease in potential difference between the plates. This is in accordance with the basic principles of electrostatics.

Now, let's consider the three points mentioned in the content:

1) It is correct that the wire strips connected to the plates of the capacitor will have the same potential as that of the plate to which they are connected. This is because they are all part of the same circuit and the potential difference between any two points in a circuit connected by ideal conductors is zero.

2) This is also correct. The potential difference between the plates of the capacitor is equal to the potential difference between the wire strips. This is because, as mentioned earlier, they are all part of the same circuit and the potential difference is the same throughout.

3) This point is where things get a bit more complicated. It is true that the potential difference is independent of path, but this is only applicable to points within the circuit. In this case, if we integrate the electric field between the wire strips, without going through the capacitor, we will indeed get the same potential difference. However, this does not necessarily mean that the potential difference between the wire strips will be reduced. It simply means that the potential difference between the two points is the same, regardless of the path taken.

Now, to address the question about the reconfiguration of charges on the wire strips when a conductor slab is introduced between the plates of the capacitor. This is a result of the redistribution of charges due to the presence of the conductor slab. When the conductor slab is introduced, the electric field between the plates is reduced and this results in a decrease in potential difference. This decrease in potential difference causes a redistribution of charges on the wire strips, leading to a reconfiguration of charges. The excess charge is still present on the wire strips, but it is now distributed differently due to the presence of the conductor slab.

In conclusion, the reconfiguration of charges on the wire strips is a result of the redistribution of charges