# The Naked Scientists Forum

### Author Topic: How does the voltage vary  (Read 2296 times)

#### syhprum

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##### How does the voltage vary
« on: 28/06/2011 20:59:54 »
If I have a capacitor comprising two vertical plates separated by a small distance between which there is a sheet dielectric materiel which increases the capacitance of the device.
If I now remove the the dielectric materiel (which of course requires the expenditure of some energy) how does the voltage betwen the plates change.
assuming the dielectric doubles the capacitance one would expect the voltage to increase 2^.5 times but what becomes of the energy used removing the dielectric.

#### Bored chemist

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##### How does the voltage vary
« Reply #1 on: 28/06/2011 21:10:00 »
It ends up stored in the capacitor.

#### syhprum

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##### How does the voltage vary
« Reply #2 on: 30/06/2011 19:55:04 »
Pondering on the question I asked does the removal of the dielectric require any energy apart from friction and gravity ?

#### Bored chemist

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##### How does the voltage vary
« Reply #3 on: 30/06/2011 20:19:25 »
Ye, in particular, it needs to provide the energy that changes the PD on the capacitor.

#### syhprum

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##### How does the voltage vary
« Reply #4 on: 30/06/2011 21:26:44 »
E=CV^2 therefore if energy has been injected into the system the voltage between the plates will rise by more than 2^.5 times.
How much ?.

Correction E=CV^2/2

« Last Edit: 01/07/2011 01:05:44 by syhprum »

#### Bored chemist

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##### How does the voltage vary
« Reply #5 on: 30/06/2011 21:48:07 »
I will have to think about that.
Let's put some numbers in. Thankfully, since this is a thought experiment I don't have to pay for the capacitor.
Lets say it's 1 farad, initially charged to one volt and the dielectric constant is 2.
There's 1 C of charge on the cap.
I take out the dielectric, and the charge says the same, but the capacitance falls to 0.5 F
So the voltage rises to 2 V

It started with 1/2 C V ^2 i.e 0.5 *1*1*1 i.e  0.5 J
It ends up with 0.5 * 0.5 *2 * 2 i.e 1 J

I must have given it the other 0.5 J of energy when I did work removing the dielectric against the electrostatic attraction between the dielectric and the plates of the cap.
Feel free to generalise this, but it seems OK to me.

#### JP

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##### How does the voltage vary
« Reply #6 on: 30/06/2011 22:26:51 »
We were just discussing something similar in new theories.  The basic answer is that a dielectric responds to the capacitor by decreasing the field within itself.  Since the square of the electric field's strength is proportional to the energy stored within it, if you decrease the field, you decrease the stored energy.

If you charge up a capacitor with a battery, disconnect it from the battery, then stick a dielectric in, the dielectric will feel a "pull" into the capacitor gap.  This can be explained by it seeking a position of lower potential energy, and this pull is the energy released.

The explanation in terms of fields is more complicated, but it's all due to the fact that the electric field of a capacitor extends beyond the edges of the plates.  When the dielectric experiences this field, it polarizes and since the field is "bowed out" from the plates at this region, the net effect is to pull on the dielectric.

The proof using fields is pretty tough, and I recall struggling with it on an exam during my undergraduate days.

#### syhprum

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##### How does the voltage vary
« Reply #7 on: 01/07/2011 00:55:23 »
This was rather what I was thinking that the problem must be caused by the spillover field at the boundary of the plates leading to an attraction to the dielectric as it is pulled out.
A more simple case would be if instead of pulling out the dielectric the capacitance was reduced by pulling the plates further apart then it would be obvious that energy had to be expended.
« Last Edit: 01/07/2011 01:32:54 by syhprum »

#### Geezer

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##### How does the voltage vary
« Reply #8 on: 01/07/2011 01:42:17 »
I had to look this up on account of the other thread that JP mentioned. It's not quite the same as removing the dielectric, but it is related.

http://en.wikipedia.org/wiki/Electrostatic_voltmeter

#### The Naked Scientists Forum

##### How does the voltage vary
« Reply #8 on: 01/07/2011 01:42:17 »