Outline Outline 4 Electrostatics 4 Electrostatics 4 Particle - - PowerPoint PPT Presentation

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• G. Ahmadi

ME 437/537

• G. Ahmadi

ME 437/537

Outline Outline

4 4Electrostatics Electrostatics 4 4Particle Charging Particle Charging 4 4Charged Particle Kinetic Charged Particle Kinetic

• G. Ahmadi

ME 437/537

Most aerosol particles carry some electrical charges Most aerosol particles carry some electrical charges

E FE q =

ne q = coul 10 6 . 1 e

19 −

× = statcoul 10 8 . 4 e

10 −

× =

c

C / Ud 3 qE πµ = d 3 qC Z u

c p

πµ = =

Coulomb Coulomb Force Force Electric Charge Electric Charge Particle Particle Mobility Mobility

• G. Ahmadi

ME 437/537

Boltzmann Boltzmann Equilibrium Charge Equilibrium Charge Distribution Distribution

∑

∞ −∞ =

− − =

n 2 2 2 2

} dkT / e n exp{ } dkT / e n exp{ ) n ( f } dkT e n exp{ dkT e ) n ( f

2 2 2

− π = µ 02 . > d } d n 05 . exp{ d 24 . ) n ( f

2

− π = µ 02 . > d

2

• G. Ahmadi

ME 437/537

Average Number of Charge Average Number of Charge µ 02 . > d

2

e dkT dn ) n ( f | n | ) n ( f | n | n π ≈ ≈ =

∫ ∑

∞ ∞ − ∞ ∞ −

2

r 4 q E π γ = ε π = γ / 4 1 = ε π = γ 4 ε ε = γ

• 1

Point Point Charge Charge cgs cgs MKS MKS

Air Air

) m ( d , d 36 . 2 n µ ≈ =

• G. Ahmadi

ME 437/537

2

r 4 q ' q E ' q F π γ = =

ε ε = γ

• 1

meter volt sec amp 10 859 . 8

12

• −

− × = ε

−

) 10 9 ( r q ' q F

9 2

× ε =

Permittivity Permittivity Coulomb’s Coulomb’s Law Law

• G. Ahmadi

ME 437/537

e 4 Ed ) 2 ) 1 ( 2 1 ]( 1 t n eZ t n eZ [ n

2 p p i i i i

+ ε − ε + + π π =

∞ ∞

∞ → + ε − ε + =

∞

t as e 4 Ed ] 2 ) 1 ( 2 1 [ n

2 p p

Quartz for 3 . 4

p =

ε

cgs cgs cgs cgs

• G. Ahmadi

ME 437/537

] t de n ) kT m 2 ( 1 ln[ e 2 dkT n

2 i 2 / 1 i 2 ∞

π + =

3 8 i

cm sec/ ion 10 ~ t n ∞

3

• G. Ahmadi

ME 437/537

• G. Ahmadi

ME 437/537

E G D

F F F u + + = dt d m

p

m q dt d τ − τ + − = τ E g u u u

p f p

m q dt d τ − = + τ E u u u

• p

p

g u uo τ + =

f

Equation Equation

• f Motion
• f Motion
• G. Ahmadi

ME 437/537

Γ − = + τ 1 u dt u d

p ^ p ^ p p ^

u u u = mu Eqτ = Γ inertia neglecting , 1 | | For >> Γ Γ − =

p ^

U m Eq up τ − = E uo || For

• G. Ahmadi

ME 437/537

Coulomb Coulomb Force Force Image Image Force Force Polarization Polarization Force Force Dipole Dipole Interactions Interactions