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# Content

`Van der Waals Forces Electron Matter Insulator and Conductor  Insulator  Conductor  A Model of a Metal  Metal in Electric Field  Drude Model of Electron Motion in a Metal Difference between Conductor and Insulator Source and Reference`

# Van der Waals Forces

Induced dipoles cause weak attraction. Electron clouds of atoms and molecules fluctuate continually. They make temporary dipoles. They see each other, fluctuate together, and attract each other more.

## Electron Matter

Electrons inside materials have their own phases of matter and phase transitions. e.g. Metal, insulator, magnet, superconductor.

## Insulator and Conductor

Insulator: charges are bound to the atoms or molecules. Conductor: charges can flow throughout the material.

### Insulator

Under a electric field, each electron shifts slightly (<1Å), but the net effect can be large. The polarization inside a material due to the total electric field is `𝑝=𝛼(𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑+𝐸𝑑𝑖𝑝𝑜𝑙𝑒𝑠)` For an insulator, `𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑≫𝐸𝑑𝑖𝑝𝑜𝑙𝑒𝑠⇒𝑝=𝛼𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑` this is also a good approximation for small 𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑 or for low density of dipoles.

### Conductor

Examples of conductors: metals, ionic solutions. Unlike insulator, charges flow like liquid in a conductor. By applying an external point charge, the original ionic equilibrium state of the conductor is broken by the electric field due to the point charge. Mobile charges inside the conductor begin to move by the exerted electric force due to the applied electric field. Polarization occurs when the moving of mobile charges begin. Mobile charges will pile up in one location and the concentration of charge will create an electric field in the region. At any location inside the conductor, the mobile charge particle always experence both the applied electric field 𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑 and the polarization electric field 𝐸𝑝𝑜𝑙𝑎𝑟. The resultant electric field 𝐸𝑛𝑒𝑡 will exert an electric force on the mobile charge and drive the mobile charge in the direction of the force. Mobile charges will move until the conductor is in equilibrium, i.e. 𝐸𝑛𝑒𝑡=0. This can be proved by contradiction. Assume 𝐸𝑛𝑒𝑡≠0 in static equilibrium. If 𝐸𝑛𝑒𝑡≠0, charges will move. This is not equilibrium. Tje assumption 𝐸𝑛𝑒𝑡≠0 is self-contradictory. Therefore 𝐸𝑛𝑒𝑡=0 inside a conductor in static equilibrium.

### A Model of a Metal

The atoms in a metal are arranged in a regular 3D lattice. The inner electrons of each metal atom are bound to the nucleus. Some of the outer electrons act as chemical bonding electrons and some of the outer electrons are mobile electron. These mobile electrons are free to move throughout the conductor and form the sea of mobile electrons of conductor. A 2D section of a unpolarizeed conductor is as following.

### Metal in Electric Field

When applying an electric field to a metal conductor, moble electron sea will shift opposite to the direction of the applied electric field. Excess charges in any conductor are always found on the surface, while the net electric field inside the conductor is still equal to zero. The net charge of the metal conductor is still equal to zero. The metal conductor can be simplified as

### Drude Model of Electron Motion in a Metal

Mobile electrons always collide with defects or wigglin atoms. Negligible net interaction between mobile electrons and forget previous velocity after collision and start a new motion at zero velocity. By the momentum principle ```∆𝑝∆𝑡=𝐹𝑛𝑒𝑡=𝑞𝐸𝑛𝑒𝑡=(−𝑒)𝐸𝑛𝑒𝑡 ∆𝑝=𝑝−0=𝑒𝐸𝑛𝑒𝑡∆𝑡 𝑣=𝑝𝑚𝑒=𝑒𝐸𝑛𝑒𝑡∆𝑡𝑚𝑒 The average velocity 𝑣=𝑒∆𝑡𝑚𝑒𝐸𝑛𝑒𝑡≡𝜇𝐸𝑛𝑒𝑡 where 𝜇 is mobility ```

## Difference between Conductor and Insulator

ConductorInsulatorMobileYesNoPolarizationEntire sea of mobile chargesIndividual atoms/moleculesStatic equilibrium𝐸𝑛𝑒𝑡=0 inside𝐸𝑛𝑒𝑡𝐸𝑎𝑝𝑝𝑙𝑖𝑒𝑑 insideExcess chargesOnly on surfaceAnywhere on or inside materialDistribution of excess chargesSpread over entire surfaceCan be in patches

## Source and Reference

ID: 191101502 Last Updated: 11/15/2019 Revision: 0

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