Material Physics Lab Report #2

 Laboratory report  THE PROPERTIES OF DIELECTRIC MATERIALS Objective:

The purpose of this experiment is to determine the capacitance of dieectric materias and reati!e  permitti!it"#  permitti!it"# Theory:

Dieectrics are materias that define most of the parameters of capacitors$ such as capacitance$ oss factor$ !ota%e capacities etc# &hen a dieectric is paced in an eectric fied$ eectric char%es do not fo' throu%h the materia as the" do in a conductor$ (ut on" si%ht" shift from their a!era%e e)uii(rium e)uii(rium positions positions causin% causin% dieectric dieectric poari*ation# poari*ation# +ecause +ecause of dieectri dieectricc poari*atio poari*ation$ n$ positi!e positi!e char%es are dispaced to'ard the fied and ne%ati!e char%es shift in the opposite direction# This creates an interna eectric fied that reduces the o!era fied 'ithin the dieectric itsef# If a dieectric is composed composed of 'ea," (onded moecues$ moecues$ those moecues moecues not on" (ecome poari*ed$ (ut aso reorient reorient so that their s"mmetr" axes ai%n to the fied# The eectric suscepti(iit" χ  suscepti(iit" χ e of a dieectric materia is a measure of ho' easi" it poari*es in response to an eectric fied# This$ in turn$ determines the reati!e permitti!it" of the materia ε =1+  χ e , ( 1) and thus infuences man" other phenomena in that medium$ from the capacitance of capacitors to the speed of i%ht# It is defined as the constant constant of proportiona proportionait" it" reatin% reatin% an eectric eectric fied  E to the induced dieectric  poari*ation densit" P densit" P such that  P= ε 0 χ e E , ( 2 ) 'here ε0 is the !acuum !a cuum permitti!it"# Commercia" manufactured capacitors t"pica" use a soid dieectric materia 'ith hi%h permitti!it" as the inter!enin% medium (et'een the stored positi!e and ne%ati!e char%es# This materia is often referred to in technica contexts as the capacitor dieectric# The capacitance of a de!ice depends on the %eometric arran%ement of the conductors# The capacitance of a parae-pate capacitor 'ith pates separated (" air can (e expressed as foo's. ε 0 εS C = , (3 ) d 'here 'here the consta constant nt ε0 is ,no'n ,no'n as the !acuum permitt permitti!i i!it" t" / 0#01 2 34-35 34-35 F6m$ S - area of each conducti!e pate$ d 7 distance (et'een the pates# If a the space (et'een the eectrodes is fied 'ith homo%eneous dieectric$ the homo%eneous eectric fied stren%th is estimated as U   E= , ( 4 ) d 'here U 7 !ota%e (et'een the eectrodes of the capacitor#

1|Page

If this space is fied 'ith an air of thic,ness d 1 and d 2 is the thic,ness of the dieectric 8see Fi%# 39$ the e)uation for the !ota%e of the capacitor (ecomes as U = E 1 d 1 + E2 d 2 , ( 5 ) From From the the eect eectro rost stat atic ics$ s$ it is ,no'n ,no'n that that the the fo foo' o'in in% % e)uait" is !aid for this case. '  ε  E1= ε E 2 , ( 6 ) Fi%# 3 'here - reati!e permitti!it" of air# +" so!in% the e)uations 819 and 8:9$ 'e %et eectric fied estimated as εU   E1= (7 ) ε d1 +ε d2 and ' 

 E2=

ε U  ' 

ε d1 +ε d 2

( 8)

In this case 8Fi%# 39 the capacitor is composed of t'o capacitors connected in series$ 'hich separate capacitances are e)ua '  ε0 ε S ε εS C 1 = ∧C 2= 0 . d1 d2 The tota capacitance is cacuated as d d 1 1 1  1 = + ∨ = 1'  + 2  . ( 9 ) C  C 1 C 2 C  ε 0 ε s ε 0 εS And the reati!e permitti!it" ε expressed from the e)uation 809 is. '  ε C  ⅆ2 ε= , ( 10 ) '  ε 0 ε S −C d 1 'here ε' is e)ua to 3 for air# Procedure:

The measur measurin% in% e)uipm e)uipment ent is consis consisted ted from from para parae e pate pate capacit capacitor or and capacit capacitance ance meter meter## The capacitance is measured in picofarads 83 pF / 34-35 F9# The !ota%e of the condenser is e)ua to ; < 8= / ; <9# > pates from dieectric materias 8P
2|Page

5# The The capaci capacita tanc ncee of the the capac capacit itor or 'as 'as meas measur ured ed## The The rea reati ti!e !e permi permitt tti! i!it it" " of the the air air 'as 'as cacuated (" usin% e)uation 8@9 and compared 'ith theoretica reati!e permitti!it" of the air# @# The thic,ness thic,ness of of dieectric dieectric pates pates 'as measure measured d (" micrometer micrometer caiper caiper## ># The or%anic or%anic %ass %ass pate pate 'as 'as added (et'een (et'een the capacitor capacitorss eectrodes eectrodes## 1# The capacitance capacitance of the capacitor capacitor 'ith 'ith a dieectric dieectric 'as measured# measured# The The reati!e reati!e permitti!it permitti!it" " of the or%anic %ass 'as cacuated (" usin% e)uation 8@9 and compared 'ith theoretica reati!e  permitti!it" of the or%anic %ass# %ass# :# The experiment experiment 'as experimen experimentt 'as repeated repeated 'ith a remainin remainin% % dieectric dieectric pates pates 8Card(oard$ 8Card(oard$ %etinax$ P
Results:

Ta(e 3# −3

d = 4 10 m

S

⋅

 Materials  Materials

d 2 ,(m)  ,(m)

d 1 ,(m)  ,(m)

C,(F)

=

3

−

9 10 ⋅

m

2

 P,  P, (C/m (C/m2 ) 4

ε

 χ 

1

2

3#44 >

4#44>

5514

3#; 1

4#;1

30@4#:

 

1.579 10

5#35 >

3#35>

3@0@#5

 

1.376 10

5#4 >

3#4>

3015#3:

 

1.76 10

5#33

3#33

3@;5#5

 

1.37 10

 E, (V/m) 3

−3

0

 Air 

40 10

Organic  glass

3.06 10

Cardboar  d 

1.77 10

2.23 10

etina! 

−3 3.2 10

0.8 10

 Pol"#in"l   Pol"#in"l  c$loride (PVC)

1.78 10

⋅

−3

⋅

−3

⋅

⋅

−3

⋅

−

20 10

−3

0.94 10 ⋅

−3

⋅

−3

⋅

−

32 10

12

⋅

−12

26 10 ⋅

34 10

−12

⋅

−3

2.22 10 ⋅

12

⋅

−12

26 10 ⋅

−10

 

7.965 10 ⋅

−8

⋅

−8

⋅

−

8

⋅

−8

⋅

d 2 7 the thic,ness of dieectric pate# d 1 7 the thic,ness of the free space (et'een capacitorBs eectrode and the d ieectric materia#

3|Page

C 7 capacit" of the capacitor is measured 'ith measurin% e)uipment# (1).

ε – 

reati!e permitti!it" of the dieectric is cacuated 'ith e)uation 8349 ' 

ε=

ε C  ⅆ2 ' 

ε 0 ε S −C d 1

.

Ex# 8or%anic %ass9 −12

εorganic glass =

1 32 10 ⋅

(8.85

−12

⋅

10

⋅

⋅

1 9.10

−3

⋅

−3

⋅

3,06 10

)−(32

⋅

⋅

10

−12

−12

⋅

0,94 10 ⋅

)

=1.975

(2)#  χ   7 eectric suscepti(iit" of a dieectric materia is cacuated 'ith e)uation 839

ε =1+  χ  Ex#

¿ > χ =ε −1

(cardboard )  χ cardboard =2.124 −1=1.124 (cardboard )

cacuated 'ith e)uation 809 (3). E 7 eectric fied stren%th of dieectric is cacuated ' 

ε U   E= '  ε d1+ ε d2 Ex# 8etinax9  E getinax =

1∙ 9 −3 −3 2.074 ∙ 0.8 ∙ 10 1 ∙ 3.2 ∙ 10

+

=1852.16

V  m

(4). P 7 dieectric  7 dieectric poari*ation densit" is cacuated 'ith e)uation 859

 P= ε 0 χ e E Ex# 8P
 P PVC = 8.85 ∙ 10

−8

∙ 1.11 ∙ 1392.2 =1.37 ∙ 10

C  m

2

Ta(e 5#

4|Page

Mteril

!theoreticl

!"rcticle

A ir

3#4441;>

3#44>

5#1 7 >

3#;1

57@

5#35>

etinax

5#1 7 :

5#4>

Po"!in" choride 8P
@#3 7 >

5#33

Or%anic %ass Card(oard

The contro 8air9 dieectricBs permitti!it" as expected 'as amost identica to the theoretica !aue# In comparison the !aues of dieectric permitti!it" in a the dieectric materia sampes are rou%h" the same# In addition$ on" the haf of the dieectric materias fit the %i!en theoretica dieectric permitti!it" !aue ran%e# These incude Card(oard 8'hich fit the ra%e perfect"9 and etinax 8'hich practica !aue is off (e a sma amount9# And the other t'o 8Or%anic %ass and P
Re$ere#ces: • •

https.66en#'i,ipedia#or%6'i,i6DieectricGCapacitors 8543:-4;-5@9 https.66en#'i,ipedia#or%6'i,i6DieectricGCapacitors 8543:-4;-5@9 https.66en#'i,ipedia#or%6'i,i6Capacitor  8543:-4;-5@9  8543:-4;-5@9

5|Page

• •

https.66accessen%ineerin%i(rar"#com6(ro'se6capacitors6c;04430>01:1ch45 8543:-4;-5@9 Laboratory work THE PROPERTIES OF DIELECTRIC MATERIALS

6|Page