1. The Physics of Electrostatic Air Cleaners
and Xerox Machines

2. 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.

3. What we know about ‘electric charges’
Charge is conserved
Charge is quantized in fundamental units of
e = 1.6 x 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

4. Electrostatic Force between two Point Charges
r = m
+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)

5. 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

6. 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

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

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

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

10. 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

11. 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

12. 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)

13. 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.

14. 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

15. 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.

16. Inside a Photocopier