introduction to electrostatic

7/30/2019 Introduction to Electrostatic

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Summary of electrostatic equations

in uniform field

2011년도 2 학기

서광석

신소재공학부 [email protected]



Application of voltage ? Subjected to an E field ?

Charge, electric field, Coulombic forces

Charge in conducting spheres ?

Behavior of charge at electrodes and dielectrics under E field ?

Real charge vs. imaginary (compensation) charge

Measured currents vs. charge motion

Charge vs. breakdown



Breakdown ?

materials have max. charge density

ex) air: breakdown strength: ~ 3.0 X 106 V/m ~ 2.64 X 10-5 C/m2

materials cannot possess higher charge density than max. charge density

excess charge should be dissipated

rate of charge dissipation:fast, sodden dissipation : breakdown

slow dissipation : no problems (no breakdown)

electron avalanche (전자사태)



Summary of electrostatic equations in uniform field

uniform Fieldnon-uniform field

by assuming that electric field & charge density are uniform,equations of electrostatics become very simple

1. Coulomb Law

two charges, q, q’, distance d in the

medium of relative dielectric const. r dielectric constant

F = force btw charges,

24

'

d

qqF

r o

Found experimentally



2. Electric field

Electric force due to a charge q’

qE F

24

'

d

q E

r o

d V E

direction

3. Capacitance① capacitance : ability to store charge

C qV V

qC / ,

q : charge, V : voltage, C : capacitance

** If a charge “feels” a(n electric) force, the charge is said to be in an electric field

+q

E

r+q



② energy stored in a capacitance

C qqV CV U 22

2

1

2

1

2

1

③ slab,

: relative dielectric constant

r

area = A

d

d

AC r o

④ isolated conducting sphere

r

r

r oC 4



⑤ parallel combination

1C

3C

2C

321 C C C C T use many layer to increase

film capacitor

T C

⑥ series combination

1C

2C

3C 321

1111

C C C C T



4. Resistance

①

Conductor :

I V R

Insulator :

R

)(V f R

constant

② resistivity

A

d R

③ conductivity

1



④ series combination

1 R

2 R

3 R

321 R R R R

⑤ parallel combination

1 R

2 R

3 R 321

1111

R R R R



5. time constant for charge decay

- time that charge will take to decay away

37%

time

charge

initially fast

later slow

: time constant ( = RC )

time taken for the charge to reachapproximately 37% of its initial value

or resistivity of materials



Example

two charges of 1 coulomb, 1 m apart

Force =2

4' d qq o

N 9121004.9)108.84(1

=

gravitational force on theobject weighing 109 kg

eq. says 1 coulomb can lift 109 kg unrealistic

so charge which can be built up in practice much less than 1 C.

practically possible

Lift a 5 mm diameter, PS sphere, 100 mg, 500 kV/m

mgqE



charge density on surface : 25105.2~ mC

charge C 9

102

)106.11(19C e

Therefore,

atomic density

Charges on the surface monolayer of atomsonly 8 atoms/million atoms.

very low value electrostatic phenomena 가 왜 unpredictable 한지 설명함

14106.1 extra electrons/ m2

19102~ atoms/m2

1 surface atoms in 125000 atoms is charged, then

surface contamination levels of few ppm can significantlychange the charge on a surface



Gauss Law

If an imaginary surface of area S is drawn round an uniform density of

charge, the component of the electric field at the surface which is

perpendicular to the surface is proportional to the total charge enclosed

mathematically

E r oS q

q

S

: charge (surface)

: area

sQS q : surface charge density



sphere, w/ surface charge density (C/m2)in air

S Q

total charge enclosed S Qq S

from Gauss law

oS oS QS S Q E )()(

breakdown strength of air = (V/m) :6103 max. E

so max. charge density

25126

max 1064.2108.8103 mC Q

a few surface atomsper million atoms

above this, breakdown of air occurswhen charges dissipate fast

this is the max. charge density in air



1 mm 간격, air, 1 eV 에너지를 갖기 위한 전압은?

diameter 1 cm2 area =23)105)((

= 251085.7 m

aird = 1 mm

air gap = 1 mm = m3101

C = capacitance =

d

Ao

= F 131095.6

1

mF / 1085.812

0

25

1085.7 m A

md 3

101



Energy W

1813210242.61095.6

2

1)(

2

1

JouleCV W

eV J 1810242.61

2169095 2V

721061.4

2169095

1 V

471079.61061.4

Volt V

∴ 1eV 의 에너지를 갖기 위해서 정도가 필요함 4

1079.6 V



Internal charge vs. surface charge

introduction to electrostatic

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