Graphing The ΔV between three charged metal electrodes

[IslandHead]

Homework Statement

Graphing The ΔV between three charged metal electrodes, in regards to x distance

Here is the the picture I'm given with the problem. The hint tells me to assume that V=0 when x=0.

Homework Equations

C=Q/ΔV

The Attempt at a Solution

I thought the electrodes looked kinda like a funky capacitor in series, so using Ceq=(1/c1+1/c2) I got ΔV=280 kV across the system. Mastering physics told me this is wrong. I am not sure if even know what equations to use on this one.

The other option maybe to use ΔV=∫Esdx where E=η/ε₀
With that ΔV=140 at 1 cm, it then should drop down to zero for 2>x>1, for electric fields can't occur in the middle of a conductor, and ΔV=0 at 3.

We didn't go over this much in class and I'm having trouble finding the relevant parts in my textbook.

I solved it:

With that ΔV=140kV at 1 cm, it then should rate of change should be to zero for 2cm>x>1cm so it goes it remains at 140kV, for electric fields can't occur in the middle of a conductor, and it goes to ΔV=0 at 3cm.

 

[anathema]

Great job on solving the problem! It's important to understand the concept of electric fields in conductors and how they affect the potential difference between electrodes. Your approach of using the integral of the electric field to calculate the potential difference is correct.

One thing to note is that the electric field is actually not zero in the middle of a conductor, but it is very small due to the high conductivity of the material. This is why the potential difference remains constant between 1cm and 2cm, as the change in electric field is negligible.

Overall, your solution shows a good understanding of the concepts involved. Keep up the good work!