# Metal rod between a capacitor

In my experiment, I am filling liquid crystal between two glass plates. Nn AC voltage is applied on them. The thickness of the liquid crystal cell is around $200 \mu m$. One glass plate is with +V and another with -V. Liquid crystal is aligned perpendicular to the electric field direction. Now I am inserting a metal coated fiber in the liquid crystal cell (between the glass plate filled with liquid crystal).

1. Is this metal coated fiber has any effect on electric field?
2. If yes, then what happens to the electric field orientation and strength.
3. Is it still transverse?
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The fiber's metal coating is a conductor, so its charges will distribute so that the electric field at its surface is perpendicular to that surface. Imagine the electric field bending towards the fiber. Unfortunately, I don't have anything quantitative at hand.

Update:

It turns out there is a standard problem (Schwartz, section 2-11) of a conducting rod of radius $a$ placed in an electric field which approaches a uniform field $E_0 \, \boldsymbol{\hat{x}}$ far from the rod, in other words that approaches an ideal capacitor field (in your problem, $2V/d \text{ , with } d \approx 200 \mu m$).

Solving in cylindrical coordinates $r,\theta,z$, with $r=0$ at the center of the rod and $x=r \cos \theta$, one gets a simple form for the potential:

$$\phi = E_0 \left[ \left(\frac{a}{r}\right)^2 - 1 \right] r \cos \theta \text{ , with } E_0 = \frac{2V}{d}$$

For $r >> a$, the potential is constant on the surfaces $r \cos \theta =$ constant, in particular: $$\phi \approx \left\{ \begin{array}{cc} +V & r \cos \theta = x = -d/2 \\ -V & r \cos \theta = x = d/2 \end{array} \right.$$

On the rod surface ($r=a$), the potential is constant ($0$). The electric field there is

$$E_{rod} = - \left. \frac{\partial \phi}{\partial r} \right|_a = 2 E_0 \cos \theta$$

The maximum field intensification factor is 2.

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