1. The document contains 28 questions and answers related to time varying fields and Maxwell's equations. It covers topics like Faraday's law, Lenz's law, motional emf, transformer emf, Maxwell's equations in differential and integral form, constitutive relations, boundary conditions, and vector wave equations.
2. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. The document provides the equations of Maxwell's equations in various forms for different materials and conditions like free space, good conductors, and harmonically varying fields.
3. Key concepts covered include displacement current, retarded potentials, phasors, and the wave nature of electromagnetic fields. Maxwell
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The AC and DC bridge both are used for measuring the unknown parameter of the circuit. The AC bridge measures the unknown impedance of the circuit. The DC bridge measures the unknown resistance of the circuit.
Dirac-delta function, Expectation values+ mathematical interpretation, Compatible observables, Incompatible observables, Difference between continuous spectra(unbound state) and line/discrete spectra(bound state), one example, including diagrams+ graphs.
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The AC and DC bridge both are used for measuring the unknown parameter of the circuit. The AC bridge measures the unknown impedance of the circuit. The DC bridge measures the unknown resistance of the circuit.
Dirac-delta function, Expectation values+ mathematical interpretation, Compatible observables, Incompatible observables, Difference between continuous spectra(unbound state) and line/discrete spectra(bound state), one example, including diagrams+ graphs.
AC bridges: Inductance and Capacitance measurementDr Naim R Kidwai
The presentation describes theory of AC bridges, inductance measurement using Maxwell bridge, Maxwell Wein bridge, Hay's bridge, Capacitance measurement using De sauty bridge, Schering bridge and working of Q meter.
Classification of signals
Deterministic and Random signals
Continuous time and discrete time signal
Even (symmetric) and Odd (Anti-symmetric) signal
Periodic and Aperiodic signal
Energy and Power signal
Causal and Non-causal signal
Representation of signals & Operation on signals
(Time Reversal, Time Shifting , Time Scaling, Amplitude scaling, Signal addition, Signal Multiplication)
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
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K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
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Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
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In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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6th International Conference on Machine Learning & Applications (CMLA 2024)
TIME-VARYING FIELDS AND MAXWELL's EQUATIONS -Unit 4 - two marks
1. Time Varying Fields and Maxwell’s Equations 4.33
TWO MARKS QUESTION AND ANSWERS
1. State Faradays law?
The induced emf in any closed path or circuit is equal to the time rate of change of
magnetic flux linking the circuit
emf
d d
V N
dt dt
N denotes the number of turns
is the flux through each turn
2. State Lenz law.
The induced current in the closed loop is in a direction such that the flux produced
by it tends to oppose the change in the original magnetic flux. This is Lenz law.
(or)
Lenz’s law states that the induced emf acts in such a way as to oppose the flux
producing it.
3. State Faradays law for a moving charge in a stationary (or) constant magnetic
field. (or) Define Motional EMF, (or) Flux cutting emf.
The Motional EMF produced by a moving conductor with a velocity, ‘v’in a constant
magnetic field ‘B’ is given by
emf
V v B dl
4. What is transformer EMF?
The emf induced in a closed path or closed circuit that is stationary while the
magnetic field B is varying with time is called as transformer emf.
emf
S
B
V E dl ds
t
5. Write the equation for point form of ohms law/Define conduction current
density.
J = E
Where is the conductivity of the material in mhos per metre ( /m), J is the
conduction current density and E is the Electric field.
2. Electromagnetic Fields
4.34
6. Define Displacement current density.
Displacement current density JD
is given by
D
D E
J
t t
Displacement current density is due to time varying electric field. Its unit is A/m2
.
7. Distinguish between transformer emf and motional emf.
Transformer emf is induced in a stationary coil with time varying magnetic field.
Example : Transformer
Motional emf is induced when the coil rotates in a constant magnetic field.
Example : Generator
8. What is the significance of displacement current?
Displacement current is a result of time varying electric field. Without displacement
current, electromagnetic wave propagation is impossible. Example of displacement
current is the current through a capacitor when an alternating voltage source is
applied to its plates.
9. Write General Maxwell’s equations in point or differential form.
D
H J
t
(Ampere’s law)
B
E
t
(Faraday’s law)
V
D
(Gauss law for Electric field)
0
B
Gauss law for Magnetic field)
10. Write the general form of Maxwell’s equations in integral form.
L S
D
H dl J ds
t
(Ampere’s law)
3. Time Varying Fields and Maxwell’s Equations 4.35
L S
B
E dl ds
t
(Gauss’s law)
V
V
S
D ds dv Q
(Gauss law for Electric field)
0
S
B ds
(Gauss law for Magnetic field)
11. Write the Maxwell’s equation for free space.
For free space = 0, V
= 0
Integral Form : Differential Form :
S
D
H dl ds
t
D
H
t
S
B
E dl ds
t
B
E
t
0
S
D ds
0
D
0
S
B ds
0
B
12. Write the Maxwell’s equation for good conductors.
For good conductors, conductivity is very high, charge density V
= 0.
Integral Form :
S
H dl J ds
S S
B
E dl ds
t
0
S
D ds
4. Electromagnetic Fields
4.36
0
S
B ds
Point Form or Differential Form :
H J
B
E
t
0
D
0
B
13. Write the Maxwell’s equations for harmonically varying fields.
Point form or Differential form :
H j E
E j H
V
D
0
B
Integral Form :
S
H dl j E ds
S
E dl j H ds
V
V
S
D ds dv
0
S
B ds
14. Time varying field is not conservative. Prove it.
For convervative field E dl
should be zero. But time varying electric field
produces a magnetic field and its value is given by Faraday’s law as,
5. Time Varying Fields and Maxwell’s Equations 4.37
.
B
E dl ds
t
So, Time varying field is not conservative.
15. Mention the parameters that limit the circuit approach for solving an electrical
problem.
Circuit theory is a two dimensional analysis. It cannot be used to calculate electric
and magnetic fields of a wave. Parameters of the medium like permittivity and
permeability are not involved in circuit approach. It cannot be used in high
frequency.
16. List the boundary conditions for time varying fields.
(i) The tangential component of Electric Field E is continuous at the boundary.
Et1
= Et2
and hence
1 1
2 2
t
t
D
D
(ii) Dn1
= Dn2
if the surface charge density is zero
Dn1
– Dn2
= S
if the surface charge density is non-zero and hence
1 2
2 1
n
n
E
E
if
the surface charge density is zero.
(iii) Ht1
– Ht2
= JS
and hence
1 2
1 2
t t
S
B B
J
where JS
is the surface current density.
.
(iv) Bn1
= Bn2
and hence
1 2
2 1
n
n
H
H
17. Write the Constitutive relations.
D E
B H
J E
6. Electromagnetic Fields
4.38
18. Define Wave.
If a physical phenomenon that occurs at one place at a given time is reproduced at
other places at later times, the time delay being proportional to the space separation
from first location, then the group of phenomena constitute a wave.
19. What is a time harmonic field?
A tiume harmonic field is one that varies periodically or sinusoidally with time.
20. Define wave number.
K
u
K is called the wave number, u is the velocity of propagation
1
u
21. What is a Phasor?
A phasor is a complex number that contains amplitude and phase information of a
sinusoidal oscillation but is independent of t.
22. What is the wavelength range of visible light?
The wavelength range of visible light is from deep red at 720 nm to voilet at 380
nm or from 0.72 um to 0.32 um corresponding to a frequency range of from 4.2
1014
Hz to 7.9 1014
Hz.
23. Why are frequencies below VLF range rarely used for wireless transmission?
Frequencies below VLF range are seldom used for wireless transmission because
huge antennas would be needed for efficient radiation of electromagnetic waves
and also because of the very low data rate at these frequencies.
24. Express E and B interms of potential functions V and A.
B A
A
E V
dt
25. Write the nonhomogenous wave equation for scalar potential V and for vector
potential A.
2
2
2
A
A J
t
7. Time Varying Fields and Maxwell’s Equations 4.39
2
2
2
v
V
V
t
26. What do you mean by a retarded potential?
1
,
4
V
V
R
t
u
V R t dV
R
is called retarded scalar potential. It indicates that
the scalar potential at a distance R from the source at time t depends on the value of
charge density at an earlier time
R
t
u
. It takes time
R
u
for the effect of to be
felt at a distance R. Hence V(R, t) is called retarted scalar potential.
Retarded vector potential is given by
1
,
4 V
R
J t
u
A R t dV
R
where
R
t t
u
= Retarded time
27. Write the source free wave equations for E and H in free space (or) write
homogenous vector wave equations.
(i)
2
2
2
0
E
E
t
(or)
2
2
2 2
1
0
E
E
u t
(ii)
2
2
2
0
H
H
t
(or)
2
2
2 2
1
0
H
H
u t
Where
2 1
u
, u is the velocity of propogation.
28. Write the homogenous vector Helmholtz’s equation for E in a simple, non
conducting, source free medium.
2
E
+ K2
E = 0
2
H
+ K2
H = 0
Where K
u