1) Magnetostatic fields are produced when charges move with constant velocity, originating from currents like those in wires.
2) Biot-Savart's law describes the magnetic field produced by a current element, with the field proportional to the current and inversely proportional to the distance.
3) Ampere's law, in integral and differential form, relates the line integral of the magnetic field around a closed path to the total current passing through the enclosed surface.
It covers all the Maxwell's Equation for Point form(differential form) and integral form. It also covers Gauss Law for Electric Field, Gauss law for magnetic field, Faraday's Law and Ampere Maxwell law. It also covers the reason why Gauss Laws are also known as Maxwell's Equation.
It covers all the Maxwell's Equation for Point form(differential form) and integral form. It also covers Gauss Law for Electric Field, Gauss law for magnetic field, Faraday's Law and Ampere Maxwell law. It also covers the reason why Gauss Laws are also known as Maxwell's Equation.
In this PPT we will study about the Transistor , symbol of transistor , types of transistor, operation of transistor , configurations of transistor, advantages of transistor and limitations of transistor.
#physicspptclub #In this video we will study about the Transistor , symbol of transistor , types of transistor, operation of transistor , configurations of transistor, advantages of transistor and limitations of transistor.
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In this PPT we will study about the Transistor , symbol of transistor , types of transistor, operation of transistor , configurations of transistor, advantages of transistor and limitations of transistor.
#physicspptclub #In this video we will study about the Transistor , symbol of transistor , types of transistor, operation of transistor , configurations of transistor, advantages of transistor and limitations of transistor.
#physicspptclub #physicsexperiments #solid state #magnetism #magneticmaterial #presentation #education #physicsfacts #scienceexperiment #presentation #education #physicsfacts #scienceexperiment #quantum #presentation #quantumphysics #bsc #msc #btech #diodecircuits #pnjunctiondiode #physicsfacts #characteristics #education #transistor #pnptransistor #npntransistor #solid state #magnetism #magneticmaterial #presentation #education #physicsfacts #scienceexperiment #presentation #education #physicsfacts #scienceexperiment #quantum #presentation #quantumphysics #bsc #msc #btech #diodecircuits #pnjunctiondiode #physicsfacts #characteristicsis #education #transistor #pnptransistor #npntransistor
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NCERT Solutions for Moving Charges and Magnetism Class 12
Class 12 Physics typically covers the topic of moving charges and magnetism, which is an essential part of electromagnetism.
For more information, visit-www.vavaclasses.com
1 ECE 6340 Fall 2013 Homework 8 Assignment.docxjoyjonna282
1
ECE 6340
Fall 2013
Homework 8
Assignment: Please do Probs. 1-9 and 13 from the set below.
1) In dynamics, we have the equation
E j Aω= − −∇Φ .
(a) Show that in statics, the scalar potential function Φ can be interpreted as a voltage
function. That is, show that in statics
( ) ( )
B
AB
A
V E dr A B≡ ⋅ = Φ −Φ∫ .
(b) Next, explain why this equation is not true (in general) in dynamics.
(c) Explain why the voltage drop (defined as the line integral of the electric field, as
defined above) depends on the path from A to B in dynamics, using Faraday’s law.
(d) Does the right-hand side of the above equation (the difference in the potential
function) depend on the path, in dynamics?
Hint: Note that, according to calculus, for any function ψ we have
dr dx dy dz d
x y z
ψ ψ ψ
ψ ψ
∂ ∂ ∂
∇ ⋅ = + + =
∂ ∂ ∂
.
2) Starting with Maxwell’s equations, show that the electric field radiated by an impressed
current density source J i in an infinite homogeneous region satisfies the equation
( )2 2 iE k E E j Jωµ∇ + = ∇ ∇⋅ + .
Then use Ampere’s law (or, if you prefer, the continuity equation and the electric Gauss
law) to show that this equation may be written as
( )2 2 1 i iE k E J j J
j
ωµ
σ ωε
∇ + = − ∇ ∇⋅ +
+
.
2
Note that the total current density is the sum of the impressed current density and the
conduction current density, the latter obeying Ohm’s law (J c = σE).
Explain why this equation for the electric field would be harder to solve than the equation
that was derived in class for the magnetic vector potential.
3) Show that magnetic field radiated by an impressed current density source satisfies the
equation
2 2 iH k H J∇ + = −∇× .
Explain why this equation for the magnetic field would be harder to solve than the
equation that was derived in class for the magnetic vector potential.
4) Show that in a homogenous region of space the scalar electric potential satisfies the
equation
2 2
i
v
c
k
ρ
ε
∇ Φ + Φ = − ,
where ivρ is the impressed (source) charge density, which is the charge density that goes
along with the impressed current density, being related by
i ivJ jωρ∇⋅ = −
Hint: Start with E j Aω= − −∇Φ and take the divergence of both sides. Also, take the
divergence of both sides of Ampere’s law and use the continuity equation for the
impressed current (given above) to show that
1 ii v
c c
E J
j
ρ
ωε ε
∇⋅ = − ∇⋅ = .
Note: It is also true from the electric Gauss law that
vE
ρ
ε
∇⋅ = ,
but we prefer to have only an impressed (source) charge density on the right-hand side of
the equation for the potential Φ. In the time-harmonic steady state, assuming a
homogeneous and isotropic region, it follows that ρv = ρvi. That is, there is no charge
3
density arising from the conduction current. (If there were no impressed current sources,
the total charge density would therefore be ze ...
Chiral Transverse Electromagnetic Waves with E H i to study Circular Dichroisminventionjournals
It is shown that a general class of transverse electromagnetic waves with E H i can be obtained. These waves possess magnetic helicity and chirality. This condition is important to excitation of nano molecules when it is necessary consider a global factor as the product of the parameter of optical chirality with the inherent enantiometric properties of the material. The absorption of a chiral molecule in a chiral electromagnetic field is proportional to the imaginary part of mixed electric-magnetic dipole polarizability of the molecules, which determines the circular dichroism, CD of molecules. Chiral fields with different handedness can be used to obtain basic information from the interaction fields-molecules with high optical chirality, having chiral hot spots in nodes of stationary waves with parallel components of electric and magnetic fields.
Ampere's Circuital Law states the relationship between the current and the magnetic field created by it. This law states that the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium.
"Impact of front-end architecture on development cost", Viktor TurskyiFwdays
I have heard many times that architecture is not important for the front-end. Also, many times I have seen how developers implement features on the front-end just following the standard rules for a framework and think that this is enough to successfully launch the project, and then the project fails. How to prevent this and what approach to choose? I have launched dozens of complex projects and during the talk we will analyze which approaches have worked for me and which have not.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
Software Delivery At the Speed of AI: Inflectra Invests In AI-Powered QualityInflectra
In this insightful webinar, Inflectra explores how artificial intelligence (AI) is transforming software development and testing. Discover how AI-powered tools are revolutionizing every stage of the software development lifecycle (SDLC), from design and prototyping to testing, deployment, and monitoring.
Learn about:
• The Future of Testing: How AI is shifting testing towards verification, analysis, and higher-level skills, while reducing repetitive tasks.
• Test Automation: How AI-powered test case generation, optimization, and self-healing tests are making testing more efficient and effective.
• Visual Testing: Explore the emerging capabilities of AI in visual testing and how it's set to revolutionize UI verification.
• Inflectra's AI Solutions: See demonstrations of Inflectra's cutting-edge AI tools like the ChatGPT plugin and Azure Open AI platform, designed to streamline your testing process.
Whether you're a developer, tester, or QA professional, this webinar will give you valuable insights into how AI is shaping the future of software delivery.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
2. Magnetostatics
If charges are moving with constant velocity, a static
magnetic (or magnetostatic) field is produced. Thus,
magnetostatic fields originate from currents (for instance,
direct currents in current-carrying wires).
Most of the equations we have derived for the electric fields
may be readily used to obtain corresponding equations for
magnetic fields if the equivalent analogous quantities are
substituted.
2
3. Magnetostatics
Biot – Savart’s Law The magnetic field intensity
dH produced at a point P by
the differential current
element Idl is proportional
to the product of Idl and the
sine of the angle α between
the element and the line
joining P to the element and
is inversely proportional to
Idl sin α the square of the distance R
dH = k
R2 between P and the element.
1
IN SI units, k = 4π , so
Idl sin α
dH = k
4πR 2
3
4. Magnetostatics
Using the definition of cross product ( A × B = AB sin θ AB an )
we can represent the previous equation in vector form as
I dl × ar I dl × R
dH = = R= R ar = R
4πR 2 4πR 3 R
The direction of d H can be determined by the right-hand rule
or by the right-handed screw rule.
If the position of the field point is specified by r and the
position of the source point by r ′
I (dl × ar ) I [dl × (r − r ′)]
dH = 2
= 3
4π r − r ′ 4π r − r ′
where er′r is the unit vector directed from the source point to
the field point, and r − r ′ is the distance between these two
points.
4
5. Magnetostatics
The field produced by
a wire can be found
adding up the fields
produced by a large
number of current
elements placed head
to tail along the wire
(the principle of
superposition).
5
6. Types of Current Distributions
• Line current density (current) - occurs for
infinitesimally thin filamentary bodies
(i.e., wires of negligible diameter).
• Surface current density (current per unit
width) - occurs when body is perfectly
conducting.
• Volume current density (current per unit
cross sectional area) - most general.
6
7. Ampere’s Circuital Law in
Integral Form
• Ampere’s Circuit Law states that the line
integral of H around a closed path
proportional to the total current through
the surface bounding the path
C
∫ H ⋅ d l = I enc
7
8. Ampere’s Circuital Law in
Integral Form (Cont’d)
dl By convention, dS is
taken to be in the
dS direction defined by the
S
right-hand rule applied
to dl.
Since volume current
density is the most
I encl = ∫ J ⋅ d s general, we can write
Iencl in this way.
S
9. Applying Stokes’s Theorem to
Ampere’s Law
∫ H ⋅ dl = ∫ ∇× H ⋅ d s
C S
= I encl = ∫ J ⋅d s
S
⇒ Because the above must hold for any
surface S, we must have
Differential form
∇× H = J
of Ampere’s Law
9
10. Ampere’s Law in Differential
Form
• Ampere’s law in differential form implies
that the B-field is conservative outside of
regions where current is flowing.
10
11. Applications of Ampere’s Law
• Ampere’s law in integral form is an integral
equation for the unknown magnetic flux
density resulting from a given current
distribution.
known
∫
C
H ⋅ d l = I encl
unknown
11
12. Applications of Ampere’s Law
(Cont’d)
• In general, solutions to integral equations
must be obtained using numerical
techniques.
• However, for certain symmetric current
distributions closed form solutions to
Ampere’s law can be obtained.
12
13. Applications of Ampere’s Law
(Cont’d)
• Closed form solution to Ampere’s law
relies on our ability to construct a suitable
family of Amperian paths.
• An Amperian path is a closed contour to
which the magnetic flux density is
tangential and over which equal to a
constant value.
13
14. Magnetic Flux Density of an Infinite
Line Current Using Ampere’s Law
Consider an infinite line current along the z-
axis carrying current in the +z-direction:
I
14
15. Magnetic Flux Density of an Infinite Line
Current Using Ampere’s Law (Cont’d)
(1) Assume from symmetry and the right-
hand rule the form of the field
H = aφ H φ
ˆ
(2) Construct a family of Amperian paths
circles of radius ρ where
0≤ρ ≤∞
15
16. Magnetic Flux Density of an Infinite Line
Current Using Ampere’s Law (Cont’d)
y
Amperian path
ρ
x
I
I encl = I
16
17. Magnetic Flux Density of an Infinite Line
Current Using Ampere’s Law (Cont’d)
(4) For each Amperian path, evaluate the
integral
C
∫ H ⋅ d l = Hl length
of Amperian
path.
magnitude of H
on Amperian
path.
∫ H ⋅ d l = Hφ 2π ρ
C
17
18. Magnetic Flux Density of an Infinite Line
Current Using Ampere’s Law (Cont’d)
(5) Solve for B on each Amperian path
I encl
H=
l
I
H = aφ
ˆ
2π ρ
18
19. Magnetic Flux Density
The magnetic flux density vector is related to the magnetic
H
field intensity by the following equation
B = µ H,
T (tesla) or Wb/m2
µ
where is the permeability of the medium. Except for
ferromagnetic materials ( such as cobalt, nickel, and iron),
µ
most materials have values of very nearly equal to that for
vacuum, µ o = 4π ⋅ 10 −7
H/m (henry per meter)
The magnetic flux through a given surface S is given by
Ψ = ∫ B ⋅ d s,
S Wb (weber)
19
20. Law of conservation
of magnetic flux
∫
s
B•ds = 0
Law of conservation of
magnetic flux or Gauss’s law
for magnetostatic field
22. There are no magnetic flow sources, and the
magnetic flux lines always close upon
themselves
23. Forces due to magnetic field
There are three ways in which force due to magnetic fields can
be experienced
1.Due to moving charge particle in a B field
2.On a current element in an external field
3.Between two current elements
23
24. Force on a Moving Charge
• A moving point charge placed in a
magnetic field experiences a force
given by
Fm = qu × B
The force experienced
by the point charge is
v B in the direction into the
Q
paper.
The force is perpendicular to the direction of charge motion,
and is also perpendicular to B .
25. Lorentz’s Force equation
If a point charge is moving in a region where both
electric and magnetic fields exist, then it experiences a
total force given by
Fe = q E Fe + Fm = F
Fm = qu × B
F = q( E + u × B)
Note: Magnetic force is zero for q moving in the
direction of the magnetic field (sin0=0)
26. Magnetic Force on a current element
One can tell if a magneto-static field is present because it
exerts forces on moving charges and on currents. If a
currentIdl B
element is located in a magnetic field , it experiences a
__
force
Id l ⇔ Q u
d= l B
FI ×
d
Idl
This force, acting on current element , is in a direction
perpendicular to the current element and also perpendicular
B B
to . It is largest when and the wire are perpendicular.
26
27. FORCE ON A CURRENT ELEMENT
• The total force exerted on a circuit C
carrying current I that is immersed in a
magnetic flux density B is given by
F = I ∫ dl × B
C
27
28. Force between two current elements
• Experimental facts: F21 F12
– Two parallel wires × ×
carrying current in I1 I2
the same direction
attract.
– Two parallel wires F21 F12
carrying current in × •
the opposite I1 I2
directions repel.
28
29. Force between two current elements
• Experimental facts:
– A short current- F12 = 0
carrying wire × I2
oriented I1
perpendicular to a
long current-
carrying wire
experiences no
force.
29
30. Force between two current elements
• Experimental facts:
– The magnitude of the force is inversely
proportional to the distance squared.
– The magnitude of the force is proportional to
the product of the currents carried by the two
wires.
30
31. Force between two current elements
• The force acting on a current element I2 dl2
by a current element I1 dl1 is given by
µ 0 I 2 d l 2 × ( I1d l 1 × aR12 )
ˆ
d (d F 12 ) =
4π 2
R12
Permeability of free space
µ0 = 4π × 10-7 F/m
31
32. Force between two current elements
• The total force acting on a circuit C2 having
a current I2 by a circuit C1 having current I1
is given by
µ 0 I1 I 2 d l 2 × ( d l 1 × aR12 )
ˆ
F 12 =
4π C2 1 ∫ C∫ R122
32
33. Force between two current elements
• The force on C1 due to C2 is equal in
magnitude but opposite in direction to the
force on C2 due to C1.
F 21 = − F 12
33