Scoring algorithm

Earlier than you determine whether or not stainless steel cookware is value shopping for, lets first talk about what stainless steel cookware is. Chrome steel is made from an alloy, or a mix of metals. Mostly, fundamental iron with chromium, nickel or some other minor metals. The chromium supplies rust protection and provides your cookware sturdiness. The nickel provides rust safety as effectively, and provides a refined look. Most effectively made chrome steel cookware has copper or aluminum added to the underside of the pan or pot. This is finished to increases the ability of the pot or pan to conduct heat.
One of the best stainless-steel cookware is the principle category, however nonetheless it is divided into several subcategories based mostly on the quality and the price range. It may be confusing to decide on the very best stainless-steel cookware out of the categories that may meet your requirements. That is where we took a step forward to explain you all the knowledge that will likely be helpful so that you can understand how to decide on the best chrome steel cookware. The best stainless-steel cookware set is manufactured from low-cost to expensive and quality constructed pots and pans.
You will find magnetic stainless steel within the layer on the outside of some high quality pieces of stainless-steel. That is to make it compatible with induction stovetops, which involve using a rapidly charging electromagnetic subject to warmth cookware. High-high quality stainless steel, like All-Clad , uses three layers of steel—the austenite layer of metal on the within, ferrite steel on the outside, and a layer of aluminum sandwiched between the two for optimum heat conductivity (metal alone doesn't conduct warmth evenly). Lesser-high quality stainless-steel is usually only one layer of austenitic chrome steel.
Aesthetically talking, chrome steel is a wise alternative when you favor to show or hang pots or pans. The clean, crisp look of all chrome steel kitchenware can remodel a mishmash of cookware into a complicated décor statement. Chrome steel kettles, such because the Cuisinart Tea Kettle will combine individual kitchenware right into a cohesive and nice entity. Take into account buying stainless-steel utensils as well. Already acquired a gorgeous stainless steel cookware assortment? The Cuisinart Chef’s Collection stainless pot rack could be the crowning glory for a kitchen, liberating up space and making these pots and pans readily accessible. Get the stainless-steel cookware of your culinary goals at Macy’s!
Arduous-anodized aluminum cookware is among the most popular forms of material, despite the fact that many people do not fairly perceive the development. Hard-anodized aluminum is plain aluminum that has been processed in a series of chemical baths charged with an electrical present. The result's a fabric that has the same superior warmth conductivity as aluminum however is non-reactive with acidic meals, similar to tomatoes, and twice as hard as chrome steel. Two drawbacks to laborious-anodized cookware are that it's not dishwasher-secure and, because it isn't magnetic, it will not work with induction range tops.
The enamel over metal method creates a piece that has the heat distribution of carbon steel and a non-reactive, low-stick surface. In the event you loved this information and you desire to acquire details about best stainless steel cookware i implore you to pay a visit to our page. Such pots are a lot lighter than most different pots of comparable dimension, are cheaper to make than chrome steel pots, and would not have the rust and reactivity problems with forged iron or carbon steel. quotation needed Enamel over metal is right for large stockpots and for different giant pans used mostly for water-primarily based cooking. Because of its mild weight and simple cleanup, enamel over metal can also be standard for cookware used while tenting. Clad aluminium or copper edit
Unique specialty cookware items served a la carte to compliment any cookware set are constructed of a sturdy Stainless Steel with a brushed exterior finish. Designed with an impression bonded, aluminum disk encapsulated base which distributes warmth quickly and evenly to permit exact temperature management. Handles are riveted for durability and efficiency. The New Specialty Cookware is compatible for all vary sorts together with induction. Along with the multi use function, another unique characteristic is bottom to top interior quantity markings in each quarts and metric measurement; and each bit comes with a tempered glass lid, oven safe to 350°F.
Whether or not you are a cooking enthusiasts, knowledgeable chef or simply cooking for your family you know the importance of getting a totally stocked kitchen. Not solely do you want the fitting elements, but you also need the right instruments to get the job performed. In any sort of fundamental cooking coaching lesson, you will be taught that chrome steel is your new finest pal when it comes to kitchen cookware. What additionally, you will study is that quality cooking tools does not normally come at a reduced price. Because of this, you will need to take good care of your cookware! Listed here are some fundamentals for stainless steel care.
To combat the uneven heating downside, most stainless steel pans are laminations of aluminum or copper on the underside to spread the warmth around, and stainless-steel contained in the pan to provide a cooking floor that's impervious to whatever you might put inside. In my experience, this chrome steel floor continues to be too sticky to fry on, and when you ever burn it you get a permanent hassle spot. But, sometimes a stainless-steel cooking surface turns out to be useful when you can't use aluminum (see below) so I keep some round. Choose one thing with a fairly thick aluminum layer on the underside.
Well, until you’re a metals professional and go examine the factory where the steel is made to see whether or not their manufacturing course of creates a pure austenite without corrosive supplies shaped, you’re not going to know for sure whether or not the craftsmanship of your stainless is of the very best quality. I think your greatest wager is to simply buy high-quality chrome steel from the start, from a brand with a reputation for good quality. But, I believe I have found out one way that you would be able to decide if the stainless cookware you already have is probably reactive. Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Built directly from Maxwell's equations, these potentials describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion, but are not corrected for quantum-mechanical effects. Electromagnetic radiation in the form of waves can be obtained from these potentials.

These expressions were developed in part by Alfred-Marie Liénard in 1898 and independently by Emil Wiechert in 1900 and continued into the early 1900s.

Implications

The study of classical electrodynamics was instrumental in Einstein's development of the theory of relativity. Analysis of the motion and propagation of electromagnetic waves led to the special relativity description of space and time. The Liénard–Wiechert formulation is an important launchpad into more complex analysis of relativistic moving particles.

The Liénard–Wiechert description is accurate for a large, independent moving particle, but breaks down at the quantum level.

Quantum mechanics sets important constraints on the ability of a particle to emit radiation. The classical formulation, as laboriously described by these equations, expressly violates experimentally observed phenomena. For example, an electron around an atom does not emit radiation in the pattern predicted by these classical equations. Instead, it is governed by quantized principles regarding its energy state. In the later decades of the twentieth century, quantum electrodynamics helped bring together the radiative behavior with the quantum constraints.

Universal Speed Limit

The force on a particle at a given location Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. and time Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. depends in a complicated way on the position of the source particles at an earlier time Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. due to the finite speed, c, at which electromagnetic information travels. A particle on Earth 'sees' a charged particle accelerate on the Moon as this acceleration happened 1.5 seconds ago, and a charged particle's acceleration on the Sun as happened 500 seconds ago. This earlier time in which an event happens such that a particle at location Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. 'sees' this event at a later time Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. is called the retarded time, Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.

There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity

This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.

A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.

If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.

Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer.. The retarded time varies with position; for example the retarded time at the Moon is 1.5 seconds before the current time and the retarded time on the Sun is 500 s before the current time. The retarded time can be calculated as:

$t_r=t-\frac{R(t_r)}{c}$

where $R(t_r)$ is the distance of the particle from the source at the retarded time. Only electromagnetic wave effects depend fully on the retarded time.

A novel feature in the Liénard–Wiechert potential is seen in the breakup of its terms into two types of field terms (see below), only one of which depends fully on the retarded time. The first of these is the static electric (or magnetic) field term that depends only on the distance to the moving charge, and does not depend on the retarded time at all, if the velocity of the source is constant. The other term is dynamic, in that it requires that the moving charge be accelerating with a component perpendicular to the line connecting the charge and the observer and does not appear unless the source changes velocity. This second term is connected with electromagnetic radiation.

The first term describes near field effects from the charge, and its direction in space is updated with a term that corrects for any constant-velocity motion of the charge on its distant static field, so that the distant static field appears at distance from the charge, with no aberration of light or light-time correction. This term, which corrects for time-retardation delays in the direction of the static field, is required by Lorentz invariance. A charge moving with a constant velocity must appear to a distant observer in exactly the same way as a static charge appears to a moving observer, and in the latter case, the direction of the static field must change instantaneously, with no time-delay. Thus, static fields (the first term) point exactly at the true instantaneous (non-retarded) position of the charged object if its velocity has not changed over the retarded time delay. This is true over any distance separating objects.

The second term, however, which contains information about the acceleration and other unique behavior of the charge that cannot be removed by changing the Lorentz frame (inertial reference frame of the observer), is fully dependent for direction on the time-retarded position of the source. Thus, electromagnetic radiation (described by the second term) always appears to come from the direction to the position of the emitting charge at the retarded time. Only this second term describes information transfer about the behavior of the charge, which transfer occurs (radiates from the charge) at the speed of light. At "far" distances (longer than several wavelengths of radiation), the 1/R dependence of this term makes electromagnetic field effects (the value of this field term) more powerful than "static" field effects, which are described by the 1/R² potential of the first (static) term and thus decay more rapidly with distance from the charge.

Existence and uniqueness of the retarded time

Existence

The retarded time is not guaranteed to exist in general. For example, if, in a given frame of reference, an electron has just been created, then at this very moment another electron does not yet feel its electromagnetic force at all. However, under certain conditions, there always exists a retarded time. For example, if the source charge has existed for an unlimited amount of time, during which it has always travelled at a speed not exceeding $v_M<c$, then there exists a valid retarded time $t_r$. To see this, consider the function $f(t^{\prime })=|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|-c(t-t^{\prime })$. At the present time, $t^{\prime }=t$, we have $f(t^{\prime })=|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|-c(t-t)=|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|\ge 0$. The derivative $f^{\prime }(t^{\prime })$ is given by

$f^{\prime }(t^{\prime })=\frac{\mathbf{r}-{\mathbf{r}}_s(t_r)}{|\mathbf{r}-{\mathbf{r}}_s(t_r)|}\cdot (-{\mathbf{v}}_s(t^{\prime }))+c\ge c-\left|\frac{\mathbf{r}-{\mathbf{r}}_s(t_r)}{|\mathbf{r}-{\mathbf{r}}_s(t_r)|}\right||{\mathbf{v}}_s(t^{\prime })|=c-|{\mathbf{v}}_s(t^{\prime })|\ge c-v_M>0$

By the mean value theorem, $f(t-\mathrm{\Delta }t)\le f(t)-f^{\prime }(t)\mathrm{\Delta }t\le f(t)-(c-v_M)\mathrm{\Delta }t$. By making $\mathrm{\Delta }t$ sufficiently large, we can force this to be negative, i.e., at some point in the past, $f(t^{\prime })<0$. By the intermediate value theorem, there exists an intermediate $t_r$ with $f(t_r)=0$, the defining equation of the retarded time. Intuitively, as the source charge moves back in time, the cross section of its light cone at present time expands faster than it can recede, so eventually it must reach the point $\mathbf{r}$. Note that this is not necessarily true if the source charge's speed is allowed to be arbitrarily close to $c$, i.e., if for any given speed $v<c$ there was some time in the past when the charge was moving at this speed. In this case the cross section of the light cone at present time approaches the point $\mathbf{r}$ as we travel back in time but does not necessarily ever reach it.

Uniqueness

For a given point $(\mathbf{r},t)$ and trajectory of the point source ${\mathbf{r}}_s(t^{\prime })$, there is at most one value of the retarded time $t_r$, i.e., one value $t_r$ such that $|\mathbf{r}-{\mathbf{r}}_s(t_r)|=c(t-t_r)$. To see this, suppose there are two retarded times $t_1$ and $t_2$, with $t_1\le t_2$. Then, $|\mathbf{r}-{\mathbf{r}}_s(t_1)|=c(t-t_1)$ and $|\mathbf{r}-{\mathbf{r}}_s(t_2)|=c(t-t_2)$. Subtracting gives $c(t_2-t_1)=|\mathbf{r}-{\mathbf{r}}_s(t_1)|-|\mathbf{r}-{\mathbf{r}}_s(t_2)|\le |{\mathbf{r}}_s(t_2)-{\mathbf{r}}_s(t_1)|$ by the triangle inequality. Unless $t_2=t_1$, this then implies that the average velocity of the charge between $t_1$ and $t_2$ is $|{\mathbf{r}}_s(t_2)-{\mathbf{r}}_s(t_1)|/(t_2-t_1)\ge c$, which is impossible. The intuitive interpretation is that we can only ever "see" the point source at one location/time at once unless it travels at least at the speed of light to another location. As the source moves forward in time, the cross section of its light cone at present time contracts faster than the source can approach, so it can never intersect the point $\mathbf{r}$ again.

We conclude that, under certain conditions, the retarded time exists and is unique.

Equations

Definition of Liénard-Wiechert potentials

The Liénard–Wiechert potentials $\phi$ (scalar potential field) and $\mathbf{A}$ (vector potential field) are for a source point charge $q$ at position ${\mathbf{r}}_s$ traveling with velocity ${\mathbf{v}}_s$:

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}{\left(\frac{q}{(1-\mathbf{n}\cdot {\mathit{\beta }}_s)|\mathbf{r}-{\mathbf{r}}_s|}\right)}_{t_r}$

and

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_{0}c}{4\pi }{\left(\frac{q{\mathit{\beta }}_s}{(1-\mathbf{n}\cdot {\mathit{\beta }}_s)|\mathbf{r}-{\mathbf{r}}_s|}\right)}_{t_r}=\frac{{\mathit{\beta }}_s(t_r)}{c}\phi (\mathbf{r},t)$

where ${\mathit{\beta }}_s(t)=\frac{{\mathbf{v}}_s(t)}{c}$ and $\mathbf{n}=\frac{\mathbf{r}-{\mathbf{r}}_s}{|\mathbf{r}-{\mathbf{r}}_s|}$.

Corresponding values of electric and magnetic fields

We can calculate the electric and magnetic fields directly from the potentials using the definitions:

$\mathbf{E}=-\mathrm{\nabla }\phi -\frac{\partial \mathbf{A}}{\partial t}$ and $\mathbf{B}=\mathrm{\nabla }\times \mathbf{A}$

The calculation is nontrivial and requires a number of steps. The electric and magnetic fields are (in non-covariant form):

$\mathbf{E}(\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}{(\frac{q(\mathbf{n}-\mathit{\beta })}{{\gamma }^2(1-\mathbf{n}\cdot \mathit{\beta }{)}^3|\mathbf{r}-{\mathbf{r}}_s{|}^2}+\frac{q\mathbf{n}\times ((\mathbf{n}-\mathit{\beta })\times \dot{\mathit{\beta }})}{c(1-\mathbf{n}\cdot \mathit{\beta }{)}^3|\mathbf{r}-{\mathbf{r}}_s|})}_{t_r}$

and

$\mathbf{B}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }{(\frac{qc(\mathit{\beta }\times \mathbf{n})}{{\gamma }^2(1-\mathbf{n}\cdot \mathit{\beta }{)}^3|\mathbf{r}-{\mathbf{r}}_s{|}^2}+\frac{q\mathbf{n}\times (\mathbf{n}\times ((\mathbf{n}-\mathit{\beta })\times \dot{\mathit{\beta }}\left)\right)}{(1-\mathbf{n}\cdot \mathit{\beta }{)}^3|\mathbf{r}-{\mathbf{r}}_s|})}_{t_r}=\frac{\mathbf{n}(t_r)}{c}\times \mathbf{E}(\mathbf{r},t)$

where $\mathit{\beta }(t)=\frac{{\mathbf{v}}_s(t)}{c}$, $\mathbf{n}(t)=\frac{\mathbf{r}-{\mathbf{r}}_s(t)}{|\mathbf{r}-{\mathbf{r}}_s(t)|}$ and $\gamma (t)=\frac{1}{\sqrt{1-|\mathit{\beta }(t){|}^2}}$ (the Lorentz factor).

Note that the $\mathbf{n}-\mathit{\beta }$ part of the first term updates the direction of the field toward the instantantaneous position of the charge, if it continues to move with constant velocity $c\mathit{\beta }$. This term is connected with the "static" part of the electromagnetic field of the charge.

The second term, which is connected with electromagnetic radiation by the moving charge, requires charge acceleration $\dot{\mathit{\beta }}$ and if this is zero, the value of this term is zero, and the charge does not radiate (emit electromagnetic radiation). This term requires additionally that a component of the charge acceleration be in a direction transverse to the line which connects the charge $q$ and the observer of the field $\mathbf{E}(\mathbf{r},t)$. The direction of the field associated with this radiative term is toward the fully time-retarded position of the charge (i.e. where the charge was when it was accelerated).

Derivation

In the case that there are no boundaries surrounding the sources, the retarded solutions for the scalar and vector potentials (SI units) of the nonhomogeneous wave equations with sources given by the charge and current densities $\rho (\mathbf{r},t)$ and $\mathbf{J}(\mathbf{r},t)$ are in the Lorenz gauge (see Nonhomogeneous electromagnetic wave equation)

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}\int \frac{\rho ({\mathbf{r}}^{\prime },{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}{d}^3{\mathbf{r}}^{\prime }$

and

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }\int \frac{\mathbf{J}({\mathbf{r}}^{\prime },{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}{d}^3{\mathbf{r}}^{\prime }$

where ${t_r}^{\prime }=t-\frac{1}{c}|\mathbf{r}-{\mathbf{r}}^{\prime }|$ is the retarded time.

For a moving point charge whose trajectory is given as a function of time by ${\mathbf{r}}_s(t^{\prime })$, the charge and current densities are as follows:

$\rho ({\mathbf{r}}^{\prime },t^{\prime })=q{\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))$

$\mathbf{J}({\mathbf{r}}^{\prime },t^{\prime })=q{\mathbf{v}}_s(t^{\prime }){\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))$

where ${\delta }^3$ is the three-dimensional Dirac delta function and ${\mathbf{v}}_s(t^{\prime })$ is the velocity of the point charge.

Substituting into the expressions for the potential gives

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}\int \frac{q{\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s({t_r}^{\prime }))}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}{d}^3{\mathbf{r}}^{\prime }$

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }\int \frac{q{\mathbf{v}}_s({t_r}^{\prime }){\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s({t_r}^{\prime }))}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}{d}^3{\mathbf{r}}^{\prime }$

These integrals are difficult to evaluate in their present form, so we will rewrite them by replacing ${t_r}^{\prime }$ with $t^{\prime }$ and integrating over the delta distribution $\delta (t^{\prime }-{t_r}^{\prime })$:

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}\iint \frac{q{\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}\delta (t^{\prime }-{t_r}^{\prime })d{t}^{\prime }{d}^3{\mathbf{r}}^{\prime }$

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }\iint \frac{q{\mathbf{v}}_s(t^{\prime }){\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}\delta (t^{\prime }-{t_r}^{\prime })d{t}^{\prime }{d}^3{\mathbf{r}}^{\prime }$

We exchange the order of integration:

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}\iint \frac{\delta (t^{\prime }-{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}q{\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))d^3{\mathbf{r}}^{\prime }d{t}^{\prime }$

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }\iint \frac{\delta (t^{\prime }-{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}^{\prime }|}q{\mathbf{v}}_s(t^{\prime }){\delta }^3({\mathbf{r}}^{\prime }-{\mathbf{r}}_s(t^{\prime }))d^3{\mathbf{r}}^{\prime }d{t}^{\prime }$

The delta function picks out ${\mathbf{r}}^{\prime }={\mathbf{x}}_s(t^{\prime })$ which allows us to perform the inner integration with ease. Note that ${t_r}^{\prime }$ is a function of ${\mathbf{r}}^{\prime }$, so this integration also fixes $t_r=t_r({\mathbf{r}}_s(t^{\prime }),t^{\prime })$.

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}\int q\frac{\delta (t^{\prime }-{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|}d{t}^{\prime }$

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }\int q{\mathbf{v}}_s(t^{\prime })\frac{\delta (t^{\prime }-{t_r}^{\prime })}{|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|}d{t}^{\prime }$

The retarded time ${t_r}^{\prime }$ is a function of the field point $(\mathbf{r},t)$ and the source point $\mathbf{x}(t^{\prime })$, and hence depends on $t^{\prime }$. To evaluate this integral, therefore, we need the identity

$\delta (f(t^{\prime }))=\sum _i\frac{\delta (t^{\prime }-t_i)}{|f^{\prime }(t_i)|}$

where each $t_i$ is a zero of $f$. Because there is only one retarded time $t_r$ for any given space-time coordinates $(\mathbf{r},t)$ and source trajectory ${\mathbf{r}}_s(t^{\prime })$, this reduces to:

$\begin{array}{rl}\delta (t^{\prime }-{t_r}^{\prime })=\frac{\delta (t^{\prime }-t_r)}{\frac{\partial }{\partial t^{\prime }}(t^{\prime }-{t_r}^{\prime }){|}_{t^{\prime }=t_r}}=& \frac{\delta (t^{\prime }-t_r)}{\frac{\partial }{\partial t^{\prime }}(t^{\prime }-(t-\frac{1}{c}|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|)){|}_{t^{\prime }=t_r}}=\frac{\delta (t^{\prime }-t_r)}{1+\frac{1}{c}(\mathbf{r}-{\mathbf{r}}_s(t^{\prime }))/|\mathbf{r}-{\mathbf{r}}_s(t^{\prime })|\cdot (-{\mathbf{v}}_s(t^{\prime })){|}_{t^{\prime }=t_r}}=\\ & =\frac{\delta (t^{\prime }-t_r)}{1-{\mathit{\beta }}_s\cdot (\mathbf{r}-{\mathbf{r}}_s)/|\mathbf{r}-{\mathbf{r}}_s|}\end{array}$

where ${\mathit{\beta }}_s={\mathbf{v}}_s/c$, and ${\mathit{\beta }}_s$ and ${\mathbf{r}}_s$ are evaluated at the retarded time, and we have used the identity $|\mathbf{x}{|}^{\prime }=\hat{\mathbf{x}}\cdot \mathbf{v}$. Finally, the delta function picks out $t^{\prime }=t_r$, and

$\phi (\mathbf{r},t)=\frac{1}{4\pi {ϵ}_0}{\left(\frac{q}{|\mathbf{r}-{\mathbf{r}}_s|(1-{\mathit{\beta }}_s\cdot (\mathbf{r}-{\mathbf{r}}_s)/|\mathbf{r}-{\mathbf{r}}_s|)}\right)}_{t_r}=\frac{1}{4\pi {ϵ}_0}{\left(\frac{q}{(1-\mathbf{n}\cdot {\mathit{\beta }}_s)|\mathbf{r}-{\mathbf{r}}_s|}\right)}_{t_r}$

$\mathbf{A}(\mathbf{r},t)=\frac{{\mu }_0}{4\pi }{\left(\frac{q\mathbf{v}}{|\mathbf{r}-{\mathbf{r}}_s|(1-{\mathit{\beta }}_s\cdot (\mathbf{r}-{\mathbf{r}}_s)/|\mathbf{r}-{\mathbf{r}}_s|)}\right)}_{t_r}=\frac{{\mu }_{0}c}{4\pi }{\left(\frac{q{\mathit{\beta }}_s}{(1-\mathbf{n}\cdot {\mathit{\beta }}_s)|\mathbf{r}-{\mathbf{r}}_s|}\right)}_{t_r}$

which are the Liénard-Wiechert potentials.

See also

• Maxwell's equations which govern classical electromagnetism
• Classical electromagnetism for the larger theory surrounding this analysis
• Relativistic electromagnetism
• Special relativity, which was a direct consequence of these analyses
• Rydberg formula for quantum description of the EM radiation due to atomic orbital electrons
• Jefimenko's equations
• Larmor formula
• Abraham-Lorentz force
• Inhomogeneous electromagnetic wave equation
• Wheeler-Feynman absorber theory also known as the Wheeler-Feynman time-symmetric theory

References

• Griffiths, David. Introduction to Electrodynamics. Prentice Hall, 1999. ISBN 0-13-805326-X.