PHYS 2421 - Fields and Wavesacademics.utep.edu/Portals/1788/physics 2421/class...
Transcript of PHYS 2421 - Fields and Wavesacademics.utep.edu/Portals/1788/physics 2421/class...
PHYS 2421 - Fields and WavesInstructor: Jorge A. López
Office: PSCI 209 A, Phone: 747-7528
Textbook: University Physics 11e, Young and Freedman
24.1 Capacitors and capacitance
24.2 Capacitors in series and parallel
24.3 Energy storage in capacitors
24.4 Dielectrics
00 0
d dq
dW F dl dq E dl dq dA
Energy needed to charge a capacitor:
In terms of energy stored in the capacitor:
2 2
0 0 00 02 2
q Q q Q
q q
q d Q d QW dq d qdq
A A A C
221 1
2 2 2
QU CV QV
C Valid for all capacitors
Energy density (per unit volume) for parallel plate capacitor
2 2 2/ 2 1 1
2 2 2Volume
Q U Q C CV QVU u
C Ad Ad Ad
In terms of E (V=Ed and C=0A/d)
202 2 2 2 2
0
/1 1 1 1
2 2 2 2
A dCV Cu E d E d E
Ad Ad Ad
22
0
1 1
2 2
CVu E
Ad
Hmwk: Problems 24.25 and 24.27 (11th or 12th Eds.)
Step 1: Charge and disconnect
Charge? 0 1 8 120 960F V CQ C V
Energy stored?0
1 1960 120 0.058
2 2C V JInitialU Q V
Step 2: Connect to an uncharged capacitor
Voltage? 0
0 1 2 1 2
1 2
96080
8 4
CV
F F
QQ Q Q CV C V V
C C
Charges:
1 1 8 80F V=640 CQ CV
2 2 4 80F V=320 CQ C V Energy:
1 2
1 1 1640 0 80 0.038
2 2 2C+32 C V JFinalU QV Q V
Energy is lost as heat in moving the charges
Electric field needed?
2
0
12
0
5
1
2
2 2 1
8.85 10
4.75 10
3 2 2
Volume
J
Volume 1m C /Nm
V/m
Uu E
UE
Hmwk: Probl. 24.30 (11th or 12th Eds.)
Soln: u=5.63x10-7 J/m3
Summary of Section 24.3
Homework for Section 24.3:
Problems 24.25, 24.27 and 24.30 (11th or 12th Eds.)
221 1
2 2 2
QU CV QV
C Energy stored in a capacitor:
Energy density:2
2
0
1 1
2 2
CVu E
Ad
Consider a capacitor with Q charges, it produces an E
200 0 0
1
2,
VE u E
d
Now, charge
it to same Q
Since medium polarizes, the net field inside is smaller
0 0 ,Inside Pol Inside DielectricVE E E E E
d
Now consider the capacitor with a polarizable medium (dielectric)
0
1
2
2
Dielectric insideu Eand its energy
is smaller
Can charge to same Q with less energy (smaller V)
Capacitance increases when using a dielectric
0Dielectric Dielectric
Dielectric
Q QV V C C
V V Since
0 0 0, , ,Q C V E , , ,Dielectric Dielectric DielectricQ C V E
The ratio
0
1DielectricCK
C , in terms of V: 0
Dielectric
VK
V
Capacitance increases when using a dielectric
Dielectric
Dielectric
Dielectric
V V
C C
E E
0K 0
An example…
Area = 2000 cm2, d=1 cm, V0=3000 V
1
12 10
0 0 2
2 108.85 10 1.77 10
1 10
2mF
m
AC
d
10 7
0 0 1.77 10 3000 5.31 10F V CQ C V
500 2
30003 10
10
VV/m
1 m
VE
d
Capacitance?
Charge?
Electric Field?
Now insert a dielectric . . .
Now insert dielectric,
voltage drops to V=1000 V
7105.31 10
5.31 101000
CF
V
QC
V
10
10
0
5.31 103.00
1.77 10
F
F
CK
C
12 11
0 3 8.85 10 2.66 10 2 2C /NmK
10
0 1.77 10 FC 75.31 10 CQ
5
0 3 10 V/mE
Capacitance?
Dielectric constant?
Permittivity
Electric Field?5
50 3 101 10
V/mV/m
3
EE
K
Again, V < V0, E < E0 and C > C0
10
0 1.77 10 FC 75.31 10 CQ
5
0 3 10 V/mE
Energy stored?
105.31 10 FC
51 10 V/mE
1000 VV 3000 VV
75.31 10 CQ
221 1
2 2 2
QU CV QV
C
2
0 0 0
10
4
1
2
11.77 10 3000
2
7.97 10
F V
F
U C V
2
10
4
1
2
15.31 10 1000
2
2.66 10
F V
F
U CV
Again, U0 > U
Homework for Section 24.4
(11th or 12th Eds.) :
Problem 24.43 a) and b) only
Problem 24.45
Problem 24.46
Solution: a) V remains unchanged, K=1.8
b) V=2 Volts
c) E0=999 N/C
E=999 N/C since the power supply was
connected during insertion of slab
Summary of Section 24.4
Capacitance increases when using a dielectric
0 0
0
1Dielectric
Dielectric Dielectric
C V EK
C V E
Dielectric
Dielectric
Dielectric
V V
C C
E E
0K
Homework for Section 24.4 (11th or 12th Eds.) :
Problem 24.43 a) and b) only, 24.45 and 24.46
PHYS 2421 - Fields and WavesInstructor: Jorge A. López
Office: PSCI 209 A, Phone: 747-7528
Textbook: University Physics 11e, Young and Freedman
24.1 Capacitors and capacitance
24.2 Capacitors in series and parallel
24.3 Energy storage in capacitors
24.4 Dielectrics