This document is a lecture on electromagnetic energy from an MIT OpenCourseWare physics course. It discusses various topics related to electromagnetic energy including: the scale of EM energy use globally and in the US; capacitive energy storage in capacitors and ultracapacitors; resistive energy loss in transmission lines and its applications like space heating; and transforming energy to and from electromagnetic forms using devices like motors and dynamos. It provides examples and equations to illustrate these concepts at a high level.
These slides present the maximum power point tracking (MPPT ) algorithms for solar (PV) systems. Later of the class we will discuss on MPPT control of wind generators.
These slides present the maximum power point tracking (MPPT ) algorithms for solar (PV) systems. Later of the class we will discuss on MPPT control of wind generators.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
2. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Electromagnetic Energy
8.21 Lecture 5
September 18, 2008
1
3. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Normal material Supplementary material
2
4. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• U. S. 2004 yearly energy use
106 EJ U. S. primary energy consumption
• 41 EJ U. S. electrical power sector
– 13 EJ distributed
– 28 EJ losses
Scale of EM energy use...
• All solar energy is transmitted to earth as
electromagnetic waves. Total yearly solar input,
1.74 × 1017
W ⇒ 5.46 × 1024
J/year
Compare total human energy consumption:
488 EJ = 4.88 × 1020
J/year ≈ 10−4
× solar input
3
5. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
*
Household electricity use (2001) (×1015
J)
Air Cond. 659
Kitchen Appl. 1098
Space Heating 418
Water Heating 375
Lighting 364
Electronics 295
(PC’s & printers 83)
†
† http://www.eia.doe.gov/emeu/reps/enduse/er01_us_tab1.html
A closer look
Electricity consumption 2005 (quads)
Generation
Transmission
Distribution
Losses 25.54
Residential 4.64
Commerical 4.32
Industrial 3.47
4
Image courtesy of Energy & Environment Directorate,
Lawrence Livermore National Library
6. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
5
7. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Outline
• The big picture
• Electric fields, forces, and work
• Review of E-field, voltage, electrical energy.
• Capacitive energy storage
• Ultracapacitors
• Resistive energy loss
• Power dissipated in a resistor
• Applications: space heating, incandescent light, transmission lines
• Transforming (to and from) electromagnetic energy
• Motors/dynamos
• Phases
• Energy storage and propagation in EM fields
Outline
• The big picture
• Electric fields, forces, and work
• Review of E-field, voltage, electrical energy.
• Capacitive energy storage
• Ultracapacitors
• Resistive energy loss
• Power dissipated in a resistor
• Applications: space heating, incandescent light, transmission lines
• Transforming (to and from) electromagnetic energy
• Motors/dynamos
• Phases
• Energy storage and propagation in EM fields
6
8. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
EMF = −N
dΦ
dt
The big picture: The roles of electromagnetic
phenomena in energy flow
• Energy “generation”
(= conversion) from fossil fuel, nuclear, hydro, etc.
– Convenient, relatively easy, and ubiquitous
– Not very efficient (Eff ! 40% at best)
7
9. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Energy Storage
– Capacitive
U =
1
2
CV 2
– Electrochemical (battery)
• Energy Transmission
– Radiative: solar, microwave
S =
1
µ0
E × B
– High voltage transmission over medium and large
distances
P = I2
R
8
10. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Energy “Use”
(= conversion) tomechanical,chemical, heatetc.
– Convenient,relatively simple, andubiquitous
– Relatively efficient
EM F = − N
dΦ
dt
P = I 2
R
9
Image of Electric Motor removed due to copyright restrictions.
See http://en.wikipedia.org/wiki/Image:Electric_motor_cycle_3.png
11. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Outline
• The big picture
• Electric fields, forces, and work
• Review of E-field, voltage, electrical energy.
• Capacitive energy storage
• Ultracapacitors
• Resistive energy loss
• Power dissipated in a resistor
• Applications: space heating, incandescent light, transmission lines
• Transforming (to and from) electromagnetic energy
• Motors/dynamos
• Phases
• Energy storage and propagation in EM fields
10
12. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Electrostatic forces are very strong:
Two Coulombs of charge separated
by 1 meter repel one another with a
force of ≈ 9 billion Newtons ≈ 2
billion pounds!
Electric fields, forces and work
Electric charges produce electric fields
Point charge
!
E =
Q
4π#0r2
r̂ SI Units:
Charge in Coulombs
Current in Amperes
Potential in Volts
Field in Volts/meter
1
4π"0
= 8.99×109
Nm2
/C2
r12
Q1 Q2
Coulomb’s Law — force
between point charges
For two point charges
F12 =
1
4π"0
Q1Q2r̂12
r2
12
Electric fields exert forces on charges
F = qE
11
13. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Work done against an electric field is stored as
electrostatic potential energy
Units of voltage are energy per unit
charge, or Joules per Coulomb.
1 Joule/Coulomb ≡ 1 Volt
Work per unit charge:
Electrostatic potential ≡ Voltage
Electric energy and potential
∆V — potential
difference between two
locations
Carry charge q from a to b along a curve C.
Work done is independent of the path,
W(a → b) = −
!
C
!
dl · !
F = −q
!
C
!
dl · !
E
= qV (b) − qV (a)
Point charge
V (r) =
Q
4π"0r
V is the electrostatic potential ⇔ the electrostatic potential energy per unit charge
12
14. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Capacitance is proportionality constant
Q = C V
“Capacity” of conductor to store charge.
• Energy stored in a capacitor:
It takes work to move each little bit of charge
through the electric field and onto the conductor.
Electromagnetic energy storage: capacitors
U =
1
2
CV 2
General idea of a capacitor:
• Place a charge Q on a conductor
• Voltage on the conductor is proportional to Q.
13
15. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Parallel plate capacitor
• Two plates, area A,
• Separation d,
• Filled with dielectric with dielectric constant
! = k!0
To increase capacitance: increase Area (size
limitations); decrease distance (charge leakage); or
increase dielectric constant (material limitations)
For parallel plates C =
!A
d
For a parallel plate capacitor with ! = k!0
C =
!A
d
=
!
8.85 × 10−12
F
"
×
k A[cm2
]
d[mm]
So typical scale for a capacitive
circuit element is pico farads:
1 picofarad = 1×10−12
14
16. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Electric field and energy storage in a parallel plate capacitor
E = 0
E
∆A
x̂
Gauss’s Law:
!
∇ · !
E =
ρ
#0
Integrate over pillbox:
!!!
V
!
∇ · !
E dV =
!!!
V
ρ
#0
dV =
1
#0
σ∆A
=
Gauss’s Law
!!
S
n̂ · !
E dS = | !
E|∆A
Energy storage: charge capacitor bit-by-bit. When charge is q, what is work needed to
move dq from bottom to top plate?
dW =
! d
0
dx !
E · !
dl =
σd
#0
dq =
d
#0A
qdq
Now integrate from q = 0 to q = Q,
W(Q) =
! Q
0
dq
d
#0A
q =
d
#0A
Q2
2
=
Q2
2C
=
1
2
CV 2
≡ U = energy stored
Charge Q, area A
Charge density
σ =
Q
A
!
E = x̂
σ
#0
15
17. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Q = CV
U =
1
2
CV 2
=
Q2
2C
=
1
2
QV
I =
dQ
dt
= C
dV
dt
Capacitor basics
[C] =
[Q]
[V ]
=
Coulombs
Volts
1
Coulomb
Volt
= 1 Farad
Capacitance units
Increase capacitance:
• Increase effective surface area: gels, nanostructures
• Increase dielectric constant (polarizable but non-conducting materials)
• Decrease effective separation
Capacitor summary:
16
18. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Using sophisticated materials technology, capable of tens or even thousands of farad
capacitors in relatively modest volumes.
“Super” or “Ultra” Capacitors
Compare with conventional rechargeable (e.g. NiMH) battery
Disadvantages
• Low total energy
• Intrinsically low voltage cell
• Voltage drops linearly with discharge
• Leakage times ranging from hours
(electrolytic) to months
Advantages
• Discharge and charge rapidly
⇒ high power
• Vastly greater number of power
cycles
• No environmental disposal
issues
• Very low internal resistance
(low heating)
Electrical energy storage?
• Batteries are expensive, heavy, involve relatively rare and unusual materials (eg.
lithium, mercury, cadmium,...), toxic.
• Storing electrical energy in capacitors is not a new idea, but using novel materials to
make “ultra” capacitors is!
17
19. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
See Problem 3
on
Assignment 2!
Introducing the Ragone Plot
18
20. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Comparison of Maxwell Technologies BCAP0120 P250 (C-cell size
super capacitor) and C-cell NiMH battery
• Max. energy density 252,000 J/kg
• Max. power density 250 – 1000 W/kg
• Max. energy density 12,900 J/kg
• Max. power density 21,500 W/kg
Voltage profiles during discharge
19
21. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Outline
• The big picture
• Electric fields, forces, and work
• Review of E-field, voltage, electrical energy.
• Capacitive energy storage
• Ultracapacitors
• Resistive energy loss
• Power dissipated in a resistor
• Applications: space heating, incandescent light, transmission lines
• Transforming (to and from) electromagnetic energy
• Motors/dynamos
• Phases
• Energy storage and propagation in EM fields
20
22. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Transmission losses — BAD
Electric space heating — GOOD??
Resistive energy loss
Electric current passing through a resistance generates heat.
• Resistive energy loss in transmission of electric power is a major impediment to
long distance energy transmission.
• Resistance converts electrical energy to heat at nearly 100% efficiency, but that’s
not the whole story.
21
23. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Resistor properties
Current and voltage in a resistor:
V = IR (Ohm’s Law)
Power in a resistor:
Carry a charge ∆Q “uphill”
through a voltage V, requires work
∆W = V ∆Q, so
dW
dt
≡ P = V
dQ
dt
= V I = I2
R = V 2
/R
22
24. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
V (t) = V0 cos ωt
I(t) = V (t)/R =
V0
R
cos ωt = I0 cos ωt
P(t) = V0I0 cos2
ωt
!P(t)" =
V 2
0
R
!cos2
ωt" =
V 2
0
2R
cos2Wt
Wt
0.5 1/2
Power dissipated in a resistor:
(DC) V &I constant P = V I =
V 2
R
= I2
R
Power dissipated in a resistor:
(AC) V &I oscillatory
23
25. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Electric Space Heating
Carbon cost to generate one kilowatt for one day:
(a) ⇒ 7.5 kg coal ⇒ 27.5 kg CO2
(b) ⇒ 2.2 m3
CH4 ⇒ 4.4 kg CO2
Moral: Electric space heat-
ing is not an environmentally
friendly choice. In fact it is
illegal in new construction in
Scandanavian countries.
Electric current run through resistance
Efficiency 100% regardless of type: light bulb, radiant coil, oil ballast
So: is electricity a good way to heat your home? Compare:
(a) Burn coal in electricity generating plant at 40% efficiency
(generous) → electricity → distribute (assuming no losses) →
space heat
(b) Directly burn natural gas (CH4) at 90% efficiency in your home
24
26. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Is essential in a world where renewable energy plays a major role
Transmission losses NEXT
Conversion losses STAY TUNED
Power lines: losses in transmission of electromagnetic energy
Transmission of energy over long distances is problematic.
• Oil & Gas — TANKERS & PIPELINE
• Coal & Nuclear — MINES & TRAINS
• Wind, solar, hydro, tidal — ELECTRICAL
So the process
WIND
SOLAR
HYDRO
conversion
−
−
−
−
−
−
−
−
→
losses
ELECTRICITY
transmission
−
−
−
−
−
−
−
−
−
→
losses
SUBSTATION
conversion
−
−
−
−
−
−
−
−
→
losses
USE
25
27. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Choice: Aluminum, often with a steel support
Cable
• Resistance grows linearly with length
• Resistance falls linearly with area
A
L
R =
ρL
A
ρ =
RA
L
[ ρ ] = [R ][A/L] = ohm-meter (Ω-m)
ρ ≡ resistivity
Resistivities:
• ρ[Cu] = 1.8 × 10−8
Ω-m
• ρ[Al] = 2.82 × 10−8
Ω-m
• ρ[Fe] = 1.0 × 10−7
Ω-m
Material properties influencing choice:
• Light: Al > Cu > Fe
• Strong: Fe > Al, Cu
• Good conductor: Cu > Al > Fe
• Not subject to significant
corrosion: Al > Cu > Fe
• Cost: Fe > Al > Cu
Design a cable
Notice resemblance to
heat conduction!
26
28. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Note that the “V ” that appears in the boxed form at
the left is the peak voltage. Often AC voltages are
quoted as root mean square. For a simple sinusoidal
voltage
VRMS =
1
√
2
Vpeak
So the boxed formula can be rewritten
Plost
P
=
PρL
AV 2
RMS
• I is current in line
• V is voltage across the load
• R is resistance in the transmission line R = ρL/A.
P = I V ⇒ I = P/V
Plost =
1
2
I2
R =
1
2
P2
V 2
R
Plost
P
=
1
2
PR
V 2
=
1
2
PρL
AV 2
For fixed material (ρ), cable (A), length,
and power, maximize the voltage
But maximum voltage is limited by other issues
like corona discharge to V ! 250 kilovolts
Note that the “V ” that appears in the boxed form at
the left is the peak voltage. Often AC voltages are
quoted as root mean square. For a simple sinusoidal
voltage
VRMS =
1
√
2
Vpeak
So the boxed formula can be rewritten
Plost
P
=
PρL
AV 2
RMS
Power loss in a transmission line
• An exercise in Ohm’s Law
• Assume AC power with “power factor” = 1/2 = !cos2
ωt"
27
29. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Specific example...
How much power can be carried in an aluminum cable
if a 7% power loss is maximum acceptable, with the
following design conditions...
L = 200 km.
A = 1 cm2
V = 200 KV
Plost
P
=
1
2
PR
V 2
=
1
2
PρL
AV 2
Then, given acceptable loss, voltage, and resistance, compute
deliverable power
Plost
P
=
PR
2V 2
⇒ P = 0.14
V 2
R
P = 0.14×
4 × 1010
V2
56Ω
≈ 100 MW
An individual cable can carry about 100 Megawatts, so a 1 Gigawatt
power plant should need about 10 such cables.
Conclusion: 7% transmission loss is probably acceptable given other inefficiencies, so
electrical transmission is a relatively efficient process.
First, calculate resistance
R =
ρL
A
= 2.82 × 10−8
Ωm ×
200 × 103
m
10−4 m2
= 56.4 Ω
28
30. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Outline
• The big picture
• Electric fields, forces, and work
• Review of E-field, voltage, electrical energy.
• Capacitive energy storage
• Ultracapacitors
• Resistive energy loss
• Power dissipated in a resistor
• Applications: space heating, incandescent light, transmission lines
• Transforming (to and from) electromagnetic energy
• Motors/dynamos
• Phases
• Energy storage and propagation in EM fields
29
31. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Dynamos/motors
• Phases and Power
• Transformers
All based on Faraday’s Law of Induction
!
C
!
E · !
dl = −
d
dt
""
S
!
B · !
dA
Long range transmission ⇒ electromagnetic forms. Hence
EM TRANSMISSION
• Dynamos/motors
MECHANICAL ENERGY
GENERATION
MECHANICAL
ENERGY USE
Transforming (to and from) Electromagnetic Energy
Basic idea: Induction
Time changing magnetic field
induces an electric field.
30
32. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
EMF = −N
dΦ
dt
Number of turns of
wire loop
Rate of change of
magnetic flux
through the loop
EMF = −N
dΦ
dt
Φ = | !
B|A cos ωt
EMF = NBAω sin ωt ≡ V0 sin ωt
EMF plays the same role in electrodynamics
as voltage in electrostatics
!
C
!
E · !
dl = −
d
dt
""
S
!
B · !
dA = −
d
dt
Φ
V0 = NBA ω
31
33. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Units and magnitudes
Magnetic flux Φ 1 Weber = 1 Volt-second
Magnetic field | !
B| 1 Tesla = 1 Weber/meter2
1 Tesla = 10,000 gauss
| !
Bearth| ≈ 0.3 gauss
Example
Generate peak 120 Volts at 60 cycles/second
B = 1000 gauss = 0.1 Weber/m2
ω = 2π × 60 sec−1
V0 = BANω ⇒ AN = 10
π m2
But remember power requirements. It you want to get
746 Watts from this generator you will need a horse
to power it!
32
34. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Phases
In AC electric circuits the current and voltage need
not be in phase, and this has enormous effects on the
power.
V (t) = V0 sin ωt
Resistive Load: I(t) = V (t)/R =
V0
R
sin ωt
!P(t)" = !I(t)V (t)"
=
!
(
V0
R
sin ωt)(V0 sin ωt)
"
= =
V 2
0
R
!sin2
ωt" =
V 2
0
2R
0 5 10 15 20 25 30
V(t)
ωt
I(t)
V(t) = I(t) R
33
35. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Capacitive Load: Q(t) = CV (t)
⇒ I(t) = C
dV
dt
= CV0ω cos ωt = CV0ω sin(ωt + π/2)
!P(t)" = !I(t)V (t)"
= !(CV0 cos ωt)(V0 sin ωt)"
= = CV 2
0 !sin ωt cos ωt" = 0 !
Current and voltage are 90◦
out of phase so no power
is delivered to load
0 5 10 15 20 25 30
V(t)
I(t)
ωt
V(t) = Q(t)/C
34
36. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
General case
R Resistance V (t) = I(t)R
C Capacitance V (t) = Q(t)/C
L Inductance V (t) = L dI/dt
Theory of impedance — domain of
electrical engineering!!
General result:
If V (t) = V0 sin ωt
Then I(t) = I0 sin(ωt − φ)
Where I0/V0 and φ depend on R, L, and C
!P(t)" = !I(t)V (t)"
= !(I0 sin(ωt + φ))(V0 sin ωt)"
= V0I0 !(sin ωt cos φ + cos ωt sin φ) cos ωt"
=
1
2
I0V0 cos φ
0 5 10 15 20 25 30
I(t)
V(t)
Wt
0 5 10 15 20 25 30
P(t) = V(t) I(t)
Wt
The ratio of actual power delivered to “naive”
power (I0V0/2) is the power factor — here cos φ.
Important issue in electrical power grids.
35
37. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
The fact that the electromagnetic power delivered to a
load in an oscillating circuit depends on the relative
phase is an example of a general phenomenon.
P(t) = !
F (t) · !
v(t)
Mechanical case is most familiar...
One child pushing another on a swing can
(a) Add energy by pushing in phase with velocity
(b) Remove energy by pushing out of phase with
velocity
(c) Do nothing by pushing a 90◦
to velocity
Phases “lite”
Phase matching is an important ingredient in
electrical power grids.
or (P(t) = V (t)I(t))
36
38. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
A huge subject...
AC ↔ DC RECTIFIERS
Low voltage ↔ High Voltage TRANSFORMERS
Phase matching POWER FACTOR
For now, some random comments
• High voltage is desirable for transmission, but
applications use a huge range of voltages,
therefore...
• Transformers occur everywhere! Even though
they are typically high efficiency (theoretically
they can approach 100%), energy losses in
transformers are significant fraction of lost
electrical energy in U. S.
• Transformers only work on AC.
• But DC has transmission advantages (stay
tuned)
Conversion of the form of EM energy
37
39. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
• Sun!
• Absorption and emission in the atmosphere & the greenhouse
effect.
• Radiative energy transport and conservation.
• Maxwell’s equations have wave solutions
Energy Storage and Propagation in EM Fields
What’s a wave?
• A fixed shape that propagates through space and time
f(x − vt).
• t → t + ∆t: f(x − vt − v∆t) has same value at
x → x + v∆t.
• v is speed of the wave.
• Electromagnetic fields propagate as waves in empty space: light!
• Electromagnetic fields store and transport energy and momentum
and exert pressure
38
40. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Wave Solution (moving up the x̂ axis):
!
E(!
x, t) = E0 cos(kx − ωt)ŷ
!
B(!
x, t) = B0 cos(kx − ωt)ẑ
Satisfy Maxwell’s equation with
prediction vwave = 1
√
µ0!0
which
equals c, the speed of light
Energy per unit volume: u(!
x, t) =
dU
dV
=
1
2
"0
!
E2
(!
x, t) +
1
2µ0
!
B2
(!
x, t)
Energy and Momentum in EM Fields
Poynting’s Vector: !
S(!
x) =⇒ Energy per unit time, per
unit area crossing a plane in the direction Ŝ at the point !
x.
!
S =
1
µ0
!
E × !
B
!
S(!
x, t)
Energy also flows as electromagnetic fields propagate ⇒ Energy flux
Conceptually similar to heat
flux from last lecture (and to
charge flux ≡ current density,
and mass flux in fluid dynamics)
v = ω/k
39
41. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Empty space: ρ = "
j = 0
Maxwell’s equations:
!
∇ · !
E = !
∇ · !
B = 0
!
∇ × !
E +
∂ !
B
∂t
= 0
!
∇ × !
B − µ0#0
∂ !
E
∂t
= 0
Substitute in Maxwell’s equations
!
∇ · !
E =
∂Ex
∂x
+
∂Ey
∂y
+
∂Ez
∂z
= 0
!
∇× !
E =
!
!
!
!
!
!
x̂ ŷ ẑ
∂
∂x
∂
∂y
∂
∂z
0 E0 cos(kx − ωt) 0
!
!
!
!
!
!
= −E0k sin(kx−ωt)ẑ
∂ !
B
∂t
= +ωB0 sin(kx − ωt)ẑ
!
∇ × !
E + ∂ !
B/∂t = (ωB0 − kE0) sin(kx − ωt)ẑ = 0
And likewise for second two Maxwell’s equations
Wave motion: ω = kvwave (or λν = vwave)
Gauss’s Law !
∇ · !
E =
ρ
#0
No magnetic charge !
∇ · !
B = 0
Faraday’s Law !
∇ × !
E +
d !
B
dt
= 0
Ampere/Maxwell Law !
∇ × !
B − µ0#0
d !
B
dt
= µ0
!
J
Maxwell’s equations have wave solutions
Wave Solution (moving up the x̂ axis):
!
E(!
x, t) = E0 cos(kx − ωt)ŷ
!
B(!
x, t) = B0 cos(kx − ωt)ẑ
40
42. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Conservation of energy: In a fixed volume,
energy change inside must come from
energy flowing in or out
Classic “conservation law”
In a fixed volume V , use Gauss’s Theorem
d
dt
!!!
V
u(!
x, t)d3
x = −
!!
boundary
of V
!
S(!
x, t) · !
dA
!!!
V
∂
∂t
u("
x, t)d3
x = −
!!!
V
"
∇ · "
S("
x, t)d3
x
∂
∂t
u("
x, t) + "
∇ · "
S("
x, t) = 0
In a time dt, an amount of energy
!
dA · !
S dt dA crosses the surface
element !
dA.
41
43. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Poynting’s vector
!
S =
1
µ0
!
E × !
B
Energy flowing in our light wave...
!
S =
1
µ0
E0 cos(kx − ωt)ŷ ×
E0
c
cos(kx − ωt)ẑ
=
!
#0
µ0
E2
0 cos2
(kx − ωt)x̂
flows in the direction perpendicular to !
E and !
B, which is direction of
wave propagation.
42
44. 8.21 Lecture 5: Electromagnetic Energy
Transforming electrical energy
Phases
EM energy propagation
Introduction: Use & big picture
Fields, forces, work, and capacitance
Electrical energy loss: resistance
Capacitance: ? Energy storage E = 1
2 CV 2
Resistance: Energy loss P =
!1
2
"
I2
R
X Space heating
! Transmission Plost
P = P R
2V 2
max
Inductance: ! Conversion Generators
Transformers
Motors
Radiation: ! Transmission S = 1
µ0
E × B
Summary
43