- The document discusses Gauss's law and electric field lines. It explains that Gauss's law relates the electric flux through a closed surface to the net electric charge enclosed by that surface.
- Electric field lines represent the direction and strength of an electric field. They originate on positive charges and terminate on negative charges. The density of field lines indicates the strength of the electric field.
- Gauss's law can be used to calculate electric fields for symmetric charge distributions. It provides an alternative formulation to Coulomb's law that is useful for problems with symmetry.
Intuitive explanation of maxwell electromagnetic equationsAbdiasis Jama
user friendly explanation of maxwell equations
For complete planning and design of microwave and cellular system, get this new book from Amazon
eBook https://www.amazon.com/dp/B0865KQG35
Paperback amazon.com/dp/B0863S4SQK
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Intuitive explanation of maxwell electromagnetic equationsAbdiasis Jama
user friendly explanation of maxwell equations
For complete planning and design of microwave and cellular system, get this new book from Amazon
eBook https://www.amazon.com/dp/B0865KQG35
Paperback amazon.com/dp/B0863S4SQK
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. EXERCISE:
Draw electric field vectors
due to the point charge
shown, at A, B and C
+ .
.
B .
A
C
Now draw field lines.
3. In this chapter you’ll learn
• To represent electric fields using
field-line diagrams
• To explain Gauss’s law and how it
relates to Coulomb’s law
• To calculate the electric fields for
symmetric charge distributions using
Gauss’s law (EASY!)
• To describe the behavior of charge
on conductors in electrostatic
equilibrium
4. 21.1 Electric Field Lines
NB For electric
field at P draw tail
of vector at point P
We can draw a vector at each point around a charged object -
• direction of E is tangent to field line (in same direction as F)
• E is larger where field lines are closer together
• electric field lines extend away from positive charge (where they
originate) and towards negative charge (where they terminate)
5. Electric field lines provide a convenient and insightful way to
represent electric fields.
– A field line is a curve whose direction at each point is the
direction of the electric field at that point.
– The spacing of field lines describes the magnitude of the field.
• Where lines are closer, the field is stronger.
Vector and field-line
diagrams of a point-
charge field
6. The field lines for
two equal positive
charges
The field lines for two charges
equal in magnitude but opposite
in sign – an electric dipole
NB the electric field vector at a point is tangent to the
field line through the point
7. Field lines for simple charge distributions
There are field lines everywhere, so every charge
distribution has infinitely many field lines.
• In drawing field-line
diagrams, we associate
a certain finite number
of field lines with a
charge of a given
magnitude.
• In the diagrams shown,
8 lines are associated
with a charge of
magnitude q.
• Note that field lines of
static charge
distributions always
begin and end on
charges, or extend to
infinity.
9. Two conducting spheres:
what is the relative sign
and magnitude of the
charges on the two
spheres?
Large sphere: 11 field lines leaving and 3
entering, net = 8 leaving
Small sphere: 8 leaving
Spheres have equal positive charge
Charge on small sphere creates
an intense electric field at
nearby surface of large sphere,
where negative charge
accumulates (3 entering field
lines).
10. Gauss’s Law
A new look at Coulomb’s Law
Flux
Flux of an Electric Field
Gauss’ Law
Gauss’ Law and Coulomb’s Law
11. A new look at Coulomb’s Law
A new formulation of Coulomb’s Law was derived
by Gauss (1777-1855).
It can be used to take advantage of symmetry.
For electrostatics it is equivalent to Coulomb’s
Law. We choose which to use depending on the
problem at hand.
Two central features are
(1) a hypothetical closed surface – a Gaussian
surface – usually one that mimics the
symmetry of the problem, and
(2) flux of a vector field through a surface
Gauss’ Law relates the electric
fields at points on a (closed)
Gaussian surface and the net
charge enclosed by that surface
12. A surface or arbitrary shape enclosing an electric
dipole.
As long as the surface encloses both charges, the
number of lines penetrating the surface from
inside is exactly equal to the number of lines
penetrating the surface from the outside, no
matter where the surface is drawn
13. A surface of arbitrary shape enclosing charges
+2q and -q. Either the field lines that end on –q do
not pass through the surface or they penetrate it
from the inside the same number of times as
from the outside.
The net number that exit is the same as that for
a single charge of +q, the net charge enclosed by
the surface.
The net number of lines out of any surface
enclosing the charges is proportional to the net
charge enclosed by the surface.
Gauss’ Law (qualitative)
15. • Electric flux quantifies the notion
“number of field lines crossing a
surface.”
– The electric flux through a flat
surface in a uniform electric field
depends on the field strength E, the
surface area A, and the angle
between the field and the normal to the
surface.
– Mathematically, the flux is given by
• Here is a vector whose
magnitude is the surface area A
and whose orientation is normal to
the surface.
21.2 Electric flux
A
cos .
EA E A
16. • When the surface is curved or the field is nonuniform, we calculate
the flux by dividing the surface into small patches , so small that
each patch is essentially flat and the field is essentially uniform over
each.
– We then sum the fluxes
over each patch.
– In the limit of infinitely many
infinitesimally small patches,
the sum becomes a
surface integral:
Electric flux with curved surfaces and
nonuniform fields
dA
d E dA
E dA
17. Flux of an electric field
Here we have an arbitrary (asymmetric)
Gaussian surface immersed in a non-uniform
electric field.
The surface has been divided up into small
squares each of area A, small enough to be
considered flat.
We represent each element of area with a
vector area A and magnitude A.
Each vector A is perpendicular to the
Gaussian surface and directed outwards
18. Electric field E may be assumed to be
constant over any given square
Vectors A and E for each square make an
angle with each other
Now we could estimate that the flux of
the electric field for this Gaussian
surface is
= E A
19. CHECKPOINT: Gaussian cube of
face area A is immersed in a
uniform electric field E that has
positive direction along z axis.
Answers:
(a) +EA
(b) –EA
(c) 0
(d) 0
In terms of E and A, what is the
flux through …..
..the front face (in the xy plane)?
A. +EA
B. 0
C. -EA
..the rear face?
A. +EA
B. 0
C. -EA
..the top face?
A. +EA
B. 0
C. -EA
..the whole cube?
A. +EA
B. 0
C. -EA
20. The flux through side B of the cube in the figure is the same
as the flux through side C. What is a correct expression for
the flux through each of these sides?
A.
B.
C.
D.
3
s
E
2
s
E
3 cos45
s
E
2 cos45
s
E
End of Lecture 5