# Homework Help: Conducter in a Parallel Capacitor

1. Sep 10, 2008

### Trenthan

So just to check i understand what i just read. from the thread "dielectric constant"

By putting a conductor e.g copper in a electric field we polarize it, and thus induce an electric field opposing the orignal field of the capacitor without it

..................................Copper in mid
Positve Plate...+.l..........l.-...........+.l..........l.-..Negative plate
....................+.l..........l.-...........+.l...........l.-
....................+.l..........l.-...........+.l...........l.-
....................+.l..........l.-...........+.l...........l.-
....................+.l..........l.-...........+.l...........l.-

Electric field.......-------> ---------> --------> (field goes through conductor in middle)
Induced field..................<--------

If the size of the induced field matched the size of the field going through the copper in the middle they would cancel and effecitvely the overall field would just be 0 in the conductor placed in the middle. So the resultant field would just be --------> ---------> effectively?

Cheers Trent
Sorry if ive broken any rules first post

**edit** had to add dots due to it colapsing the spaces and it was just a bunch of lines and letters sry its made it alot harder to understand

2. Sep 10, 2008

### Defennder

Yes you're right. The E-field in a conductor at electrostatic equilibrium is zero. Although I sometimes wonder what would happen if we applied an E-field whose magnitude exceeds all that of the electrons of the conductor combined. Clearly the E-field in the conductor would be non-zero, no?

3. Sep 10, 2008

### Trenthan

you raise a very interesting point, ill have to think about that one hmmm......

4. Sep 10, 2008

### Trenthan

while on the topic of a conductor in the field wouldnt it be correct to say the capacitance would be

If we use C=(e0*A)/w

e0=8.85*10-12,

"w" is width from positive plate to negative plate, therefore since the field cancels in the middle couldnt we just substitute (w/2) into C=(e0*A)/w, **assuming that the width of the copper inside the field is half "w/2", therefore "w/4" lies on both sides of the copper inbetween the plates (lets assume it air for simplicity).

The copper inside the field doesnt contribute towards capactiance, since there is no electric field therefore no potential differance inside the copper.

So in this case capactiance would in fact increase by adding in the copper, since "w" has decreased thus capacitance is higher. However, this is where im confussed, doesnt it only increase if it is a insulator in the capacitor, and also since there is nolonger a potential in the copper wouldnt it infact decrease?????? goes with the idea a conductor lowers capacitance

5. Sep 10, 2008

### Trenthan

Sorry about posting a post after a post but it wouldnt let me edit anything in for some reason

Just curious a conductor in between two parallel plates lets say the plate width was 6mm, and a 2mm conductor is inserted**

Therefore the capacitance C=(e0*A)/d

Lets say A is 1 to make it easier
Therefore C = (e0*1)/.004, in every case and it doesnt matter if the conducter is in the middle, touching the left plate, or the right plate does it???. Capacitance is the same in all conditions

Got this from this website hopefully it is correct if some1 could just double check that its realiable it seems reliable from what ive read from it http://dev.physicslab.org/Document....ctrostatics_DielectricsBeyondFundamentals.xml

Cheers TRent