ANURAG TYAGI CLASSES (ATC) is an organisation destined to orient students into correct path to achieve
success in IIT-JEE, AIEEE, PMT, CBSE & ICSE board classes. The organisation is run by a competitive staff comprising of Ex-IITians. Our goal at ATC is to create an environment that inspires students to recognise and explore their own potentials and build up confidence in themselves.ATC was founded by Mr. ANURAG TYAGI on 19 march, 2001.
ANURAG TYAGI CLASSES (ATC) is an organisation destined to orient students into correct path to achieve
success in IIT-JEE, AIEEE, PMT, CBSE & ICSE board classes. The organisation is run by a competitive staff comprising of Ex-IITians. Our goal at ATC is to create an environment that inspires students to recognise and explore their own potentials and build up confidence in themselves.ATC was founded by Mr. ANURAG TYAGI on 19 march, 2001.
The following presentation explain about electric charge ,its properties and methods of charging a body .the presentation also explain electrostatic force
Learning Objectives
Define electric charge, and describe how the two types of charge interact.
Desribe three common situations that generate static electricity. State the law of conservation of charge.
Describe three methods for charging an object.
State Coulomb’s law
Describe an electric field diagram of a positive point charge; of a negative point charge with twice the magnitude of positive charge
Draw the electric field lines between two points of the same charge; between two points of opposite charge.
Thank you So much
Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.
A geometrical model of the electron is illustrated. Pair production and annihilation processes is described. Origin of electric charge and the the fine structure constant reviewed. Quantum mechanical description of electric and magnetic field lines at the Planck scale is depicted
The following presentation explain about electric charge ,its properties and methods of charging a body .the presentation also explain electrostatic force
Learning Objectives
Define electric charge, and describe how the two types of charge interact.
Desribe three common situations that generate static electricity. State the law of conservation of charge.
Describe three methods for charging an object.
State Coulomb’s law
Describe an electric field diagram of a positive point charge; of a negative point charge with twice the magnitude of positive charge
Draw the electric field lines between two points of the same charge; between two points of opposite charge.
Thank you So much
Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.
A geometrical model of the electron is illustrated. Pair production and annihilation processes is described. Origin of electric charge and the the fine structure constant reviewed. Quantum mechanical description of electric and magnetic field lines at the Planck scale is depicted
Describes electrostatic principles and concepts.
**More good stuff available at:
www.wsautter.com
and
http://www.youtube.com/results?search_query=wnsautter&aq=f
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.
Richard's entangled aventures in wonderlandRichard 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.
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.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Comparing Evolved Extractive Text Summary Scores of Bidirectional Encoder Rep...University of Maribor
Slides from:
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Track: Artificial Intelligence
https://www.etran.rs/2024/en/home-english/
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.
What is greenhouse gasses and how many gasses are there to affect the Earth.
Chapter 1: Electrostatics
1. Chapter 3 - Electrostatics
Understanding electrical charges
of its characters and phenomena
2. Electrical charge
3.1
• Explain electrical charge, positive and negative charges,
conductors and insulators, charge and discharge, conservation of
charges and quantization of charges.
Two plastic rods being rubbed by fur and two glass rods beingTwo plastic rods being rubbed by fur and two glass rods being
rubbed by silkrubbed by silk
silk
fur
plastic
rod A
plastic
rod A
glass
rod C
glass
rod D
3. When two plastic rods are brought closer to each other, the result ofWhen two plastic rods are brought closer to each other, the result of
will be…will be…
Both rods repel each other.Both rods repel each other.
rod A rod B
4. As two glass rods are brought closer to each other, …As two glass rods are brought closer to each other, …
both rods repel each other.both rods repel each other.
rod C
rod D
5. However, as a plastic rod is brought closer to a glass rod, …However, as a plastic rod is brought closer to a glass rod, …
both rods attract each otherboth rods attract each other..
rod C
rod B
6. When the fur is brought closer to the hanging glass rod, …When the fur is brought closer to the hanging glass rod, …
both items attract each other.both items attract each other.
furThe rod initial
position
The rod final position
7. As the silk is brought closer to the hanging plastic rod, …As the silk is brought closer to the hanging plastic rod, …
Both items attract each other.Both items attract each other.
silk
The rod initial
position
The rod final position
8. The rubbing of the items cause theThe rubbing of the items cause the electrical chargeselectrical charges to transfer fromto transfer from
one material to another.one material to another.
What is anWhat is an electrical chargeelectrical charge??
In nature, it can be either a positive charge or a negative charge.In nature, it can be either a positive charge or a negative charge.
A crude representation of an atom, showing the positively chargedA crude representation of an atom, showing the positively charged
nucleus at its center and the negatively charged electrons orbiting aboutnucleus at its center and the negatively charged electrons orbiting about
it.it.
The structure of atoms can beThe structure of atoms can be
described in terms of three particles;described in terms of three particles;
electron, proton and neutron.electron, proton and neutron.
9. A unit of an electrical charge is coulomb, CA unit of an electrical charge is coulomb, C
An electron has a magnitude of e = -1.6x10An electron has a magnitude of e = -1.6x10-19-19
C.C.
Likewise, a proton has a magnitude of e = +1.6x10Likewise, a proton has a magnitude of e = +1.6x10-19-19
C.C.
It would take 1/e = 6.3 x 10It would take 1/e = 6.3 x 101818
protons to create a total charge of +1C.protons to create a total charge of +1C.
Likewise, it would take 6.3 x 10Likewise, it would take 6.3 x 101818
electrons to create a total charge ofelectrons to create a total charge of
-1C.-1C.
The identical charges repel each other.The identical charges repel each other.
However, the opposite charges attract each other.However, the opposite charges attract each other.
initialfinal
finalinitial
10. The two plastic rods acquired negative charges.The two plastic rods acquired negative charges.
Since both rods have similar charges, they repel each other.Since both rods have similar charges, they repel each other.
Rod A
Rod B initial
position
Rod B final
position
11. Therefore, the glass rod acquires ________ charges.Therefore, the glass rod acquires ________ charges.
The fur acquires ________ charges.The fur acquires ________ charges.
The silk acquires _________ charges.The silk acquires _________ charges.
Negative or positive charges?Negative or positive charges?
positivepositive
positivepositive
negativenegative
13. The experiment conducted by BenjaminThe experiment conducted by Benjamin
Franklin (1706 – 1790) showed that theFranklin (1706 – 1790) showed that the
electrical charges were conserved.electrical charges were conserved.
Principle of conservation of charge:Principle of conservation of charge:
The sum of all the electricThe sum of all the electric
charges in any closed system ischarges in any closed system is
constant.constant.
15. Quantization of Electrical charge
3.1.1
In 1909, Robert Millikan discovered the existence of electrical charge isIn 1909, Robert Millikan discovered the existence of electrical charge is
in discreet amount or a packet. The electric charge cannot be dividedin discreet amount or a packet. The electric charge cannot be divided
into amounts smaller than the charge of one electron or proton.into amounts smaller than the charge of one electron or proton.
N = 3
N = ???
Number of charges = 3
Number of charges = ????
16. Free electrons in conductor or insulator
3.1.2
Charges or free electrons can move freely in conductor. When certainCharges or free electrons can move freely in conductor. When certain
amount of charges are transferred to the conductor, the charges areamount of charges are transferred to the conductor, the charges are
uniformly distributed to the other parts of conductor.uniformly distributed to the other parts of conductor.
Metals and alloys are normally good conductor.Metals and alloys are normally good conductor.
Certain chemical solution like NaClCertain chemical solution like NaCl displays good conductor.displays good conductor.
17. Substances like glass, Perspex, silk and rubber are good insulators.Substances like glass, Perspex, silk and rubber are good insulators.
When an insulator is rubbed, the rubbed part contains charges.When an insulator is rubbed, the rubbed part contains charges.
Charges cannot be transferred to the other parts of the insulator.Charges cannot be transferred to the other parts of the insulator.
This part is still neutral
18. Charging by induction
3.1.3
In the induction process of charging, a charged object requires noIn the induction process of charging, a charged object requires no
contact with the object inducing the charge.contact with the object inducing the charge.
Grounding
the charge
19. Coulomb’s Law
3.2
• State Coulomb’s Law and use equation F=Qq/4πε0r2
for a point
charge and system.
In 1785, Charles Coulomb (1736 -1806) established theIn 1785, Charles Coulomb (1736 -1806) established the
fundamental law of electric force between two stationary chargedfundamental law of electric force between two stationary charged
particles.particles.
It applies only to point charges and to spherical distributions ofIt applies only to point charges and to spherical distributions of
charges. The vector F can be written as:charges. The vector F can be written as:
r
r
qq
kF 2
21
21
=
20. Suppose there are two charges, qSuppose there are two charges, q11 and qand q22 at a distance, r. If theat a distance, r. If the
two charges have the same sign, both will repel each other with atwo charges have the same sign, both will repel each other with a
force, F.force, F.
r
FORCE
q1 q2
Electrical charge in focusThis repulsive electrical force is a vector. It is written asThis repulsive electrical force is a vector. It is written as FF2121..
21. Likewise, if qLikewise, if q11 has negative sign and qhas negative sign and q22 has positive sign, both willhas positive sign, both will
attract each other with a force, F.attract each other with a force, F.
r
FORCE
q1 q2
Electrical charge in focusThis attractive electrical force is a vector. It is written asThis attractive electrical force is a vector. It is written as FF2121..
22. Suppose there are three charges, qSuppose there are three charges, q11, q, q22 and qand q33..
The resultant force due to qThe resultant force due to q11 andand
qq22 on qon q33 will be Fwill be FTT..
q2
q1
q3
F31
F32
FT
It can be said that FIt can be said that FTT is a vectoris a vector
addition of Faddition of F3131 and Fand F3232..
23. The Coulomb force is aThe Coulomb force is a field forcefield force – a force exerted by one– a force exerted by one
object on another even though there is no physical contactobject on another even though there is no physical contact
between them.between them.
The magnitude of force on charge qThe magnitude of force on charge q22 can be written as:can be written as:
2
21
21
r
qq
kF = F21
q1 q2
25. Electric Field
3.3
• Define the electric field strength E=F/q and describe the electricDefine the electric field strength E=F/q and describe the electric
field lines for isolated point charge, dipole charges and plate offield lines for isolated point charge, dipole charges and plate of
uniform charges.uniform charges..
An electric field exists in theAn electric field exists in the
region of space around aregion of space around a
charged object. When anothercharged object. When another
charged object enters thischarged object enters this
electric field, the field is whatelectric field, the field is what
exerts a force on the secondexerts a force on the second
charged object.charged object.
26. +
Q
q0
E
test charge
+ + + + +
+ + + + + + +
+ + + + + + +
+ + + + + +
+ +
0q
F
E =
We define the electric field at the location of the small test chargeWe define the electric field at the location of the small test charge
to be the electric force acting on it divided by the charge qto be the electric force acting on it divided by the charge q00 of theof the
test charge.test charge.
27. Suppose there are two charges, qSuppose there are two charges, q11 and qand q22..
The resultant electric field due toThe resultant electric field due to
qq11 and qand q22 at point C will be Eat point C will be ETT..
q2
q1
C
E2
ET
It can be said that EIt can be said that ETT is a vectoris a vector
addition of Eaddition of E11 and Eand E22..
E1
28. Michael Faraday introduced the electric field lines in the followingMichael Faraday introduced the electric field lines in the following
manner:manner:
The electric field vector E is tangent to the electric fieldThe electric field vector E is tangent to the electric field
lines at each point.lines at each point.
The number of lines per unit area through a surfaceThe number of lines per unit area through a surface
perpendicular to the lines is proportional to the strengthperpendicular to the lines is proportional to the strength
of the electric field in a given region.of the electric field in a given region.
For a positive point charge, the lines radiate outward and for aFor a positive point charge, the lines radiate outward and for a
negative point charge, the lines converge inward.negative point charge, the lines converge inward.
E is large when the field lines are close together and small when theyE is large when the field lines are close together and small when they
are far apart.are far apart.
Electric Field Lines
3.3.1
29. Electric field of positiveElectric field of positive
and negative pointand negative point
chargescharges
Two dimensional drawing contains only the field lines that lie in theTwo dimensional drawing contains only the field lines that lie in the
plane containing the point charge.plane containing the point charge.
Electric field of positiveElectric field of positive
point charges.point charges.
30. Moving charge in a uniform electric field
3.3.2
• Describe quantitatively the motion of a charge in a uniform electric
field.
A charged particle in the electric field experiences electricalA charged particle in the electric field experiences electrical
force,force, FF = q= q EE. The charged particle also accelerates as. The charged particle also accelerates as
dictated by second Newton’s Law,dictated by second Newton’s Law, FF = m= maa..
Thus, the accelerationThus, the acceleration
of charged particle isof charged particle is
written:written:
m
qE
a =
31. Gauss’ Law
3.4
Consider a uniform electric field passing through an area thatConsider a uniform electric field passing through an area that
is perpendicular to the field.is perpendicular to the field.
• State and use Gauss’ Law to determine the electric field of a
charged body.
Electric flux exists as
electric field flows
through the area
32. Electric flux,Electric flux, ΦΦ is defined asis defined as
A.E=Φ
If the area A is parallel to the field lines, E = 0; thus, Ф = 0.
No electric flux exists as
no electric field pierce
the area.
33. If the E lines pierce at the area A at an angle θ away from the
normal line, the flux is written:
θcosA.E=Φ
normal line
E
θ
35. Gauss Theorem
3.4.1
Consider a point charge q and a
spherical surface of radius r from
centre on the charge. The constant
magnitude of electric field on the
surface of the sphere is written:
2
r
q
kE =
Since the electric field is everywhere
perpendicular to the spherical surface,
the electric flux will be :
0
2
2
0
Q
r4
r4
Q
A.E
ε
π
πε
=
==Φ
36. For any type of surface, the general
flux equation through a close surface
can be written :
0
Q
dA.E
ε
==Φ ∫
Therefore, it is equally true for any
surface that encloses the charge q, the
flux would simply be the charge divided
by the permittivity of free space :
37. 3.4.2
The equivalence of Gauss’ Law and Coulomb’s Law
Consider a point charge q with a spherical Gaussian surface of radius
r from centre on the charge. The Gauss’ law states that the flux
through a close surface:
0
Q
dA.E
ε
==Φ ∫
The close surface area, ∫dA = 4πr2
.
The electric field, E for the charge:
0
2 Q
)r4.(E
ε
π =
2
0r4
Q
E
πε
=
38. The positive test charge exerts electrical force due to the electric field.
The magnitude of electrical force is written:
E.qF 0=
Finally, transformation of Gauss’ law to Coulomb’s law is simply written
as:
2
0
0
r4
Q
.qF
πε
=
40. 3.4.3
Sphere of concentrated charges
Consider positive electric charge Q is distributed uniformly throughout
the volume of an insulating sphere with radius R.
Since the charge density is
constant,
33
R
3
4
q
r
3
4
'q
ππ
=
The equation is simplified into:
3
3
R
r
q'q =
41. The electric field enclosed by the surface is considered as if that
enclosed charge were concentrated at the center.
2
0r4
'q
E
πε
=
From substitution of q’, we can get the electric field enclosed by the
surface.
r
R4
q
E 3
0
=
πε
42. 3.4.4
Electric field of charged thin spherical shell
Consider a charged spherical shell of total charge
q and two concentric spherical surfaces, S1 and
S2.
For r ≥ R, the electric field is:
2
0r4
q
E
πε
=
For r < R, the electric field is:
0E =
43. 3.4.5
Electric field of infinite charged line
Consider λ = Q/L for uniformly distributed charge along an infinitely long,Consider λ = Q/L for uniformly distributed charge along an infinitely long,
thin wire. Gaussian surface of a cylinder with arbitrary radius r andthin wire. Gaussian surface of a cylinder with arbitrary radius r and
arbitrary length L is used. No flux through the ends because E lies in thearbitrary length L is used. No flux through the ends because E lies in the
plane of the surface. E has the same value everywhere on the cylinderplane of the surface. E has the same value everywhere on the cylinder
walls. The area, A = 2πrL. The electric field for the cylinder iswalls. The area, A = 2πrL. The electric field for the cylinder is:
+ + + + + + + + + + + + +
r
L
r2
1
E
0
λ
πε
=
44. 3.4.6
Electrical field of infinite charged sheet
Consider σ is the density of charge perConsider σ is the density of charge per
unit area. Therefore Q =σ A. Theunit area. Therefore Q =σ A. The
charged sheet passes through thecharged sheet passes through the
middle of cylinder’s length, so themiddle of cylinder’s length, so the
cylinder’s ends are equidistant from thecylinder’s ends are equidistant from the
sheet. No flux passes through thesheet. No flux passes through the
cylinder’s side walls, therefore, E = 0.cylinder’s side walls, therefore, E = 0.
The total flux in Gauss’s law, Φ = 2EAThe total flux in Gauss’s law, Φ = 2EA
since EA from each cylinder’s end. Thus,since EA from each cylinder’s end. Thus,
the electric field for the infinite planethe electric field for the infinite plane
sheet of charge is written:sheet of charge is written:
+ + + + +
+ + + + +
+ + + + +
+ + + + +
+ + + + +
+ + + + +
EE
02
E
ε
σ
=
45. 3.5.1
Electric equipotential surface
The potential at various points in an electric field can be visualized byThe potential at various points in an electric field can be visualized by
equipotential surfaces. Equipotential surface is three dimensionalequipotential surfaces. Equipotential surface is three dimensional
surface on which the electric potential V is the same at every point. Ifsurface on which the electric potential V is the same at every point. If
the test charge qthe test charge q00 is moved from a point to point on such a surface,is moved from a point to point on such a surface,
the electric potential energy qthe electric potential energy q00V remains constant.V remains constant. Field lines andField lines and
equipotential surfaces are always mutually perpendicular.equipotential surfaces are always mutually perpendicular.
Equipotential
surface
Field line
+
+ -
46. 3.5
Electric potential
Consider a system of charges. VConsider a system of charges. V11 is theis the
potential at point P from a charge qpotential at point P from a charge q11. The. The
work done to bring charge qwork done to bring charge q22 to point Pto point P
from infinity without acceleration is equalfrom infinity without acceleration is equal
to qto q22VV11. As the two charges are. As the two charges are
separated at distance r, the work done isseparated at distance r, the work done is
equal to the potential energy. The workequal to the potential energy. The work
done to bring the charge Q from a to bdone to bring the charge Q from a to b
is:is:
W = Q(VW = Q(Vaa –V–Vbb) = -ΔU.) = -ΔU.
• Define the electric potential and use equation V=Q/4Define the electric potential and use equation V=Q/4πεπε00r.r.
• Use relation E = - dV/dr.Use relation E = - dV/dr.
• Understand the relationship between electric potential and potential energy.Understand the relationship between electric potential and potential energy.
dr
r
1
Q
4
1
V 2
0
∫=
πε
==
r
qq
4
1
WU 21
0πε
