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`Electric Potential at a Single Point Potential inside a Metal Potential Difference in an Insulator  Dielectric Constant Source and Reference`

# Electric Potential at a Single Point

Potential of finite systems of charges at a single point 𝐴 is the potential relative to infinite separation. `𝑉𝐴≡𝑉𝐴-𝑉∞` By convention, the potential at infinity is equal to zero.
The potential of a point charge `𝑉𝑟≡𝑉𝑟-𝑉∞=−𝑟∫∞𝐸∙𝑑𝑙=−𝑟∫∞14𝜋𝜀0𝑞𝑥2𝑑𝑥=14𝜋𝜀0𝑞𝑥𝑟｜∞=14𝜋𝜀0𝑞𝑟 (volts)` While the electric potential energy of two particles is `𝑈ele=14𝜋𝜀0𝑞1𝑞2𝑟12𝑑𝑥 (joules)` The relationship of potential difference and electric field can be expressed as `𝐸=−𝑑𝑉𝑑𝑥=−∇𝑉; ∆𝑉=−𝑓∫𝑖𝐸∙𝑑𝑙` Therefore, knowing 𝐸 at only one point does not tell 𝑉 at that point. And knowing 𝑉 at that point does not tell 𝐸.

## Potential inside a Metal

For a metal in equilibrium, the eletric field inside is 𝐸=0, and the potential is constant. when a metal is in equilibrium, electron sea inside the metal is in equilibrium also, that is the velocity 𝑣net=0. When a metal is out of equilibrium, /for examples, applied current, ie hooked up in a circuit. or immediately after aplying a field i.e. electrons move to screen it.

## Potential Difference in an Insulator

The electric field in capacitor filled with insulator is equal to ```𝐸net=𝐸plates+𝐸dipoles where 𝐸plates=const in capacitor; 𝐸dipoles=𝑓(𝑥,𝑦,𝑧) ∆𝑉=−𝑏∫𝑎𝐸∙𝑑𝑥 ``` The electric field in insulator composes of two components. Field from the charges on plates and field from the induced dipoles. The average field from induced dipoles is opposite to the field from the plates. When a charged particle moving from 𝐴 to 𝐵, 𝐸dipoles is sometimes parallel to 𝑑𝑥 and sometimes is antiparallel to 𝑑𝑥.
Considering the path due to polarized insulator outside the insulator. ```𝐸∙𝑑𝑙≥0 ∆𝑉=𝑉𝐵−𝑉𝐴=−𝑏∫𝑎𝐸∙𝑑𝑙 ```

### Dielectric Constant

Dielectric medium has a constant 𝐾. Inside the insulating medium 𝐸net=𝐸applied𝐾. The bigger 𝐾 is the more it dampens the electric field. In other words, a bigger 𝐾 means greater polarization. Dielectric constant for various insulators: vacuum1 by definition air1.0006 typical plastic5 NaCl6.1 water80 strontium titanate310

## Source and Reference

ID: 191200702 Last Updated: 12/7/2019 Revision: 0

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