# Potential difference between the parallel metal plates

• jamesjenson
In summary, the conversation discusses the change in potential difference between two parallel metal plates initially placed 2mm apart and then separated by 1 cm after being connected to a 9V battery. The conversation mentions different ways to calculate potential difference, including using the concept of constant potential or constant electric field. It is also noted that the area of the plates does not change, allowing for the use of the formula C = Q/V. The final conclusion is that the new potential difference between the plates is 45V.
jamesjenson

## Homework Statement

Two metal plates are placed in parallel, 2mm apart. They are then connected to a fully charged 9V battery. Without discharging the plates, the battery is removed, after which the separation between them is increased to 1 cm. What is the new potential difference between the parallel metal plates?

E=Vd E= Q/4ε∏r2

## The Attempt at a Solution

I have no clue whatsoever, the prof never even went over this, just a hint in the right direction would be apperaited

Ask yourself: with the battery removed, will the potential difference stay constant? Will the charge on each plate (and therefore electric field)?

There are several ways to find potential difference. If potential remains constant, use the one involving that. If electric field remains constant, use the one involving that instead.

schaefera said:
Ask yourself: with the battery removed, will the potential difference stay constant? Will the charge on each plate (and therefore electric field)?

There are several ways to find potential difference. If potential remains constant, use the one involving that. If electric field remains constant, use the one involving that instead.

Ok, so if there battery is removed then, and the plates don't touch anything, they would keep their charge, no? So the only change would be the distance between them?

jamesjenson said:
Ok, so if there battery is removed then, and the plates don't touch anything, they would keep their charge, no? So the only change would be the distance between them?

Yes, they keep their charge. It might also help to remember $E = \frac{\sigma}{\epsilon_0}$

Fluxthroughme said:
Yes, they keep their charge. It might also help to remember $E = \frac{\sigma}{\epsilon_0}$

ok, but doesn't {\sigma} mean Q/A ? and I don't have any info on the area of the plates here

jamesjenson said:
ok, but doesn't {\sigma} mean Q/A ? and I don't have any info on the area of the plates here

The point is that the area of the plates doesn't change. So if both Q and A stay the same, so does sigma, and we know $\epsilon_0$ is a constant.

Fluxthroughme said:
The point is that the area of the plates doesn't change. So if both Q and A stay the same, so does sigma, and we know $\epsilon_0$ is a constant.

ahhh! Ok, I don't see why I didnt see that, thanks!

Can we use the concept of capacitance here in this example :

C = eA/d
and
C = Q/V

I think that as "d" would be increased 5 times then "C" would decrease by five times.

As C decreases by 5 times then (since charge "Q" on the plates is conserved) "V" would increase by five times .

Thus (new) V = 45 V

Does that not satisfy all the electrostatics principles ?

## 1. What is potential difference between parallel metal plates?

The potential difference between parallel metal plates is the difference in electric potential between the two plates. It is also known as voltage and is measured in volts (V).

## 2. How is the potential difference between parallel metal plates calculated?

The potential difference between parallel metal plates can be calculated by dividing the work done (in joules) in moving a unit of positive charge from one plate to the other by the magnitude of that charge (in coulombs).

## 3. What causes potential difference between parallel metal plates?

The potential difference between parallel metal plates is caused by the separation of positive and negative charges on the plates. This creates an electric field between the plates, which exerts a force on any charged particles in the vicinity.

## 4. How does the distance between parallel metal plates affect the potential difference?

The potential difference between parallel metal plates is directly proportional to the distance between the plates. As the distance increases, the electric field weakens and the potential difference decreases. This relationship is known as Coulomb's Law.

## 5. What is the role of potential difference between parallel metal plates in electrical circuits?

The potential difference between parallel metal plates is an essential component in electrical circuits. It allows for the flow of electric current from one plate to the other, powering devices and enabling the transfer of energy. It is also used as a means of storing and transferring electrical energy in batteries and capacitors.

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