The Physics of Electrostatic Air Cleaners and Xerox Machines

Preliminaries…. Not all things can be explained by gravity, mechanical forces: Shocking your self by touching doorknobs, car doors. Hair-raising experiences Lighting a flourescent lamp while walking on a carpet Observed ‘Repulsion’ & Strength of Attraction’ Postulate: 1. Presence of ‘charges’(2 types: positive & negative) that flow from 1 object to another 2. Opposite charges attract (pull). Like charges repel (push) 3. Forces increase with decreasing separation.

What we know about ‘electric charges’ Charge is conserved Charge is quantized in fundamental units of e = 1.6 x 10 -19 Coulombs Charge is intrinsic to matter: Sub-atomic particles: electrons have q = - e protons have q = + e What does it mean to have a net charge ? Net charge is the sum of an object’s +,- charges. Just because an object is negatively-charged doesn’t mean it has no + charges Normally, objects have neutral charge (equal +, - charges) How does one normally ‘charge’ an object ? By rubbing against a different material Connecting to one side of a battery

Electrostatic Force between two Point Charges r = 10 -10m +q1 +q2 proportional to the magnitude of charges inversely proportional to the square of the separation F = k q1 q2 / r2 Coulomb’s Law where k = 9 x109 N-m2/C2 (Coulomb’s constant) Electrostatic force is much stronger than gravitational force! Example: F(electrostatic between 2 electrons) = (9x109N-m2/C2)(1.6x10-19C) )(1.6x10-19C)/(10-10m)2 = 23 x 10-9 N (electrostatic) Fgravitational = (6.67x10-11 N-m2/kg2)(9.1x10-31kg)2/(10-10m)2 = 55 x 10-52N (grav)

Charges in Conductors (metals) Charges in metals move to the surface and disperse from each other Applications: Shielded Rooms E = 0 Charges can discharge to the environment: - Charges on sharp corners can leap, escape onto air molecules - ‘Corona discharge’ – accompanied by ‘glowing’, happens with high humidity. - can be discharged by ‘touching’ - Ionization: spark of arc forms Everyday Applications: Lightning Rods

Can objects attract/repel even if they are neutral ? + charged still neutral induced polarization attraction ! + - + Yes, the opposite charges are closer than the like charges and the effect is thus, attraction ! Everyday examples: neutral hair close to a charged comb negatively-charged dust sticking to a neutral wall or surface

Problem: Undesirable Air Particles in Factories, Hospitals, etc. Solution: Use an Electrostatic Precipitator or Filter

Application 1: Electrostatic Air Cleaners Dust particles charged negatively in air charged using high voltage and collected on positively- charged metal plates

Application 2 : The Xerox Machine First Photocopy 1938 Chester Carlson made the prototype photocopier First commercial photocopier

What are Electric Fields ? Two Ways of Viewing Charge – Charge Interactions: q2 q1 1. Charge q1 feels a force due to charge q2. + 2. Charge q1 feels a force due its interaction with an electric field E set up by charge q2. E – magnitude proportional to the generating charge q2 direction at a point is in the direction of the force felt by a unit + test charge at point + + q1 E q2

Particles in Nature Fermions: Bosons: Photons electrons, protons, neutrons - 1 indistinguishable fermion/wave - follow’s Pauli’s exclusion principle Bosons: Photons - indistinguishable bosons can share waves Applications: lasers, superconductors Let’s look at electrons flowing in solids travel like waves in a solid, w/ specific energy levels occupy each level two at a time: Spin up and spin down electrons levels filled from lowest to highest energy levels form ‘bands’: valence band (highest level is Fermi level) beyond valence band is conduction band

Metals vs. Insulators vs. Semiconductors Metals - have empty levels above Fermi energy levels Analogy of electron flow in metals: Like guests in a partly-filled 1-floor theatre, electrons readily move, responding to applied electric fields Energy Fermi level (ground floor) Energy filled level vacant level 2 Insulators – no empty levels near Fermi level Analogy: Ground floor is full. High balcony. electrons can’t respond to forces Conduction bands (high balcony) Valence band: filled (ground floor)

3. Semiconductors – narrow gap between valence & conduction 3. Semiconductors – narrow gap between valence & conduction bands; poor insulators/conductors at room temp. Analogy: Guests in a theatre with low balcony Conduction band (low balcony) Energy (light or Heat) Valence band Electrons can hop into the low ‘balcony’ and move. (gap is smaller) Application: Photoconductors in Xerox Machines insulating in the dark conducting in the light: Light in the form of photons, give energy for electrons to bridge gap.

The Xerox Process - Corona discharge - - - - - - - - - - photoconductor - - - - - - - - - - + + + + + + + + Photoconductor is coated with negative charge Light Light - - - - - - - + + + + + + + + - - Exposure to light from original erases charge to form a charge image. charge image - - - - - - - + + + + + - - - - - - - toner particles - - - - - - - + + + + + - - - - - - - Charge image attracts + charged toner particles

Light Charge image is erased to release the toner particles - - - - - - - Negatively charged paper - - - - - - - - - - - - - - - - - - - The toner is transferred to negatively- charged paper - - - - - - - - - - - - Heat Toner is fused to paper by heat. Copy is now done. Cycle is then repeated. - - - - - - -

Inside a Photocopier