Tuesday 2 October 2012
Electric potential
Not to be confused with Electric potential energy.
Electromagnetism
In classical electromagnetism, the electric potential (a scalar quantity denoted by φ, φE or V and also called the electric field potential or the electrostatic potential) at a point is equal to the electric potential energy (measured in joules) of a charged particle at that location divided by the charge (measured in coulombs) of the particle. The electric potential is independent of the test particle's charge - it is determined by the electric field alone. The electric potential can be calculated at a point in either a static (time-invariant) electric field or in a dynamic (varying with time) electric field at a specific time, and has the units of joules per coulomb, or volts.
There is also a generalized electric scalar potential that is used in electrodynamics when time-varying electromagnetic fields are present. This generalized electric potential cannot be simply interpreted as the ratio of potential energy to charge, however.
INTRODUCTION
Objects may possess a property known as an electric charge. An electric field exerts a force on charged objects, accelerating them in the direction of the force, in either the same or the opposite direction of the electric field. If the charged object has a positive charge, the force and acceleration will be in the direction of the field. This force has the same direction as the electric field vector, and its magnitude is given by the size of the charge multiplied with the magnitude of the electric field. Classical mechanics explores the concepts such as force, energy, potential etc. The electric potential (or potential) at a point in an electric field is defined as the work done in moving a unit positive charge from infinity to that point.
Force and potential energy are directly related. As an object moves in the direction that the force accelerates it, its potential energy decreases. For example, the gravitational potential energy of a cannonball at the top of a hill is greater than at the base of the hill. As the object falls, that potential energy decreases and is translated to motion, or inertial (kinetic) energy.
For certain forces, it is possible to define the "potential" of a field such that the potential energy of an object due to a field is dependent only on the position of the object with respect to the field. Those forces must affect objects depending only on the intrinsic properties of the object and the position of the object, and obey certain other mathematical rules.
Two such forces are the gravitational force (gravity) and the electric force in the absence of time-varying magnetic fields. The potential of an electric field is called the electric potential. The synonymous term "electrostatic potential" is also in common use.
The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
[edit]In electrostatics
The electric potential at a point r in a static electric field E is given by the line integral
where C is an arbitrary path connecting the point with zero potential to r. When the curl ∇ × E is zero, the line integral above does not depend on the specific path C chosen but only on its endpoints. In this case, the electric field is conservative and determined by the gradient of the potential:
Then, by Gauss's law, the potential satisfies Poisson's equation:
where ρ is the total charge density (including bound charge) and ∇· denotes the divergence.
The concept of electric potential is closely linked with potential energy. A test charge q has an electric potential energy UE given by
The potential energy and hence also the electric potential is only defined up to an additive constant: one must arbitrarily choose a position where the potential energy and the electric potential are zero.
These equations cannot be used if the curl ∇ × E ≠ 0, i.e., in the case of a nonconservative electric field (caused by a changing magnetic field; see Maxwell's equations). The generalization of electric potential to this case is described below.
[edit]Electric potential due to a point charge
The electric potential created by a point charge Q, at a distance r from the charge (relative to the potential at infinity), can be shown to be
where ε0 is the electric constant (permittivity of free space). This is known as the Coulomb Potential.
The electric potential due to a system of point charges is equal to the sum of the point charges' individual potentials. This fact simplifies calculations significantly, since addition of potential (scalar) fields is much easier than addition of the electric (vector) fields.
The equation given above for the electric potential (and all the equations used here) are in the forms required by SI units. In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.
[edit]Generalization to electrodynamics
When time-varying magnetic fields are present (which is true whenever there are time-varying electric fields and vice versa), it is not possible to describe the electric field simply in terms of a scalar potential V because the electric field is no longer conservative: is path-dependent because ∇ × E ≠ 0 (Faraday's law of induction).
Instead, one can still define a scalar potential by also including the magnetic vector potential A. In particular, A is defined to satisfy:
where B is the magnetic field. Because the divergence of the magnetic field is always zero due to the absence of magnetic monopoles, such an A can always be found. Given this, the quantity
is a conservative field by Faraday's law and one can therefore write
where V is the scalar potential defined by the conservative field F.
The electrostatic potential is simply the special case of this definition where A is time-invariant. On the other hand, for time-varying fields, note that
unlike electrostatics.
Note that this definition of V depends on the gauge choice for the vector potential A (the gradient of any scalar field can be added to A without changing B). One choice is the Coulomb gauge, in which we choose ∇ · A = 0. In this case, we obtain
where ρ is the charge density, just as for electrostatics. Another common choice is the Lorenz gauge, in which we choose A to satisfy
[edit]Units
The SI unit of electric potential is the volt (in honor of Alessandro Volta), which is why electric potential is also known as voltage. Older units are rarely used nowadays. Variants of the centimeter gram second system of units included a number of different units for electric potential, including the abvolt and the statvolt.
[edit]Galvani potential versus electrochemical potential
Main article: Galvani potential
Inside metals (and other solids and liquids), the energy of an electron is affected not only by the electric potential, but also by the specific atomic environment that it is in. When a voltmeter is connected between two different types of metal, it measures not the electric potential difference, but instead the potential difference corrected for the different atomic environments.[1] The quantity measured by a voltmeter is called electrochemical potential or fermi level, while the pure unadjusted electric potential is sometimes called Galvani potential. The terms "voltage" and "electric potential" are a bit ambiguous in that, in practice, they can refer to either of these in different contexts.
FISAPHI
Tuesday 21 August 2012
Reaping a Multiple Reward
For every disciplined effort, there are multiple rewards. Thats one of life's great arrangements. In fact, it’s an extension of the Biblical law that says that if you sow well, you will reap well.
Here’s a unique part of the Law of Sowing and Reaping. Not only does it suggest that we’ll all reap what we’ve sown, it also suggests that we’ll reap much more. Life is full of laws that both govern and explain behaviors, but this may well be the major law we need to understand: for every disciplined effort, there are multiple rewards.
What a concept! If you render unique service, your reward will be multiplied. If you’re fair and honest and patient with others, your reward will be multiplied. If you give more than you expect to receive, your reward is more than you expect. But remember: the key word here, as you might well imagine, is discipline.
Everything of value requires care, attention and discipline. Our thoughts require discipline. We must consistently determine our inner boundaries and our codes of conduct, or our thoughts will be confused. And if our thoughts are confused, we will become hopelessly lost in the maze of life. Confused thoughts produce confused results.
Remember the law: “For every disciplined effort, there are multiple rewards.” Learn the discipline of writing a card or a letter to a friend. Learn the discipline of paying your bills on time, arriving to appointments on time, or using your time more effectively. Learn the discipline of paying attention, or paying your taxes or paying yourself. Learn the discipline of having regular meetings with your associates, or your spouse, or your child, or your parent. Learn the discipline of learning all you can learn, of teaching all you can teach, of reading all you can read.
For each discipline, multiple rewards. For each book, new knowledge. For each success, new ambition. For each challenge, new understanding. For each failure, new determination. Life is like that. Even the bad experiences of life provide their own special contribution. But a word of caution here for those who neglect the need for care and attention to life’s disciplines: everything has its price. Everything affects everything else. Neglect discipline, and there will be a price to pay. All things of value can be taken for granted with the passing of time.
That’s what we call the Law of Familiarity. Without the discipline of paying constant, daily attention, we take things for granted. Be serious. Life’s not a practice session.
If you’re often inclined to toss your clothes onto the chair rather than hanging them in the closet, be careful. It could suggest a lack of discipline. And remember, a lack of discipline in the small areas of life can cost you heavily in the more important areas of life. You cannot clean up your company until you learn the discipline of cleaning your own garage. You cannot be impatient with your children and be patient with your distributors or your employees. You cannot inspire others to sell more when that goal is inconsistent with your own conduct. You cannot admonish others to read good books when you don’t have a library card.
Think about your life at this moment. What areas need attention right now? Perhaps you’ve had a disagreement with someone you love or someone who loves you, and your anger won’t allow you to speak to that person. Wouldn’t this be an ideal time to examine your need for a new discipline? Perhaps you’re on the brink of giving up, or starting over, or starting out. And the only missing ingredient to your incredible success story in the future is a new and self-imposed discipline that will make you try harder and work more intensely than you ever thought you could.
The most valuable form of discipline is the one that you impose upon yourself. Don’t wait for things to deteriorate so drastically that someone else must impose discipline in your life. Wouldn’t that be tragic? How could you possibly explain the fact that someone else thought more of you than you thought of yourself? That they forced you to get up early and get out into the marketplace when you would have been content to let success go to someone else who cared more about themselves.
Your life, my life, the life of each one of us is going to serve as either a warning or an example. A warning of the consequences of neglect, self-pity, lack of direction and ambition… or an example of talent put to use, of discipline self-imposed, and of objectives clearly perceived and intensely pursued.
-What are your thoughts on the ideas above? What areas of your life can you improve in?
Here’s a unique part of the Law of Sowing and Reaping. Not only does it suggest that we’ll all reap what we’ve sown, it also suggests that we’ll reap much more. Life is full of laws that both govern and explain behaviors, but this may well be the major law we need to understand: for every disciplined effort, there are multiple rewards.
What a concept! If you render unique service, your reward will be multiplied. If you’re fair and honest and patient with others, your reward will be multiplied. If you give more than you expect to receive, your reward is more than you expect. But remember: the key word here, as you might well imagine, is discipline.
Everything of value requires care, attention and discipline. Our thoughts require discipline. We must consistently determine our inner boundaries and our codes of conduct, or our thoughts will be confused. And if our thoughts are confused, we will become hopelessly lost in the maze of life. Confused thoughts produce confused results.
Remember the law: “For every disciplined effort, there are multiple rewards.” Learn the discipline of writing a card or a letter to a friend. Learn the discipline of paying your bills on time, arriving to appointments on time, or using your time more effectively. Learn the discipline of paying attention, or paying your taxes or paying yourself. Learn the discipline of having regular meetings with your associates, or your spouse, or your child, or your parent. Learn the discipline of learning all you can learn, of teaching all you can teach, of reading all you can read.
For each discipline, multiple rewards. For each book, new knowledge. For each success, new ambition. For each challenge, new understanding. For each failure, new determination. Life is like that. Even the bad experiences of life provide their own special contribution. But a word of caution here for those who neglect the need for care and attention to life’s disciplines: everything has its price. Everything affects everything else. Neglect discipline, and there will be a price to pay. All things of value can be taken for granted with the passing of time.
That’s what we call the Law of Familiarity. Without the discipline of paying constant, daily attention, we take things for granted. Be serious. Life’s not a practice session.
If you’re often inclined to toss your clothes onto the chair rather than hanging them in the closet, be careful. It could suggest a lack of discipline. And remember, a lack of discipline in the small areas of life can cost you heavily in the more important areas of life. You cannot clean up your company until you learn the discipline of cleaning your own garage. You cannot be impatient with your children and be patient with your distributors or your employees. You cannot inspire others to sell more when that goal is inconsistent with your own conduct. You cannot admonish others to read good books when you don’t have a library card.
Think about your life at this moment. What areas need attention right now? Perhaps you’ve had a disagreement with someone you love or someone who loves you, and your anger won’t allow you to speak to that person. Wouldn’t this be an ideal time to examine your need for a new discipline? Perhaps you’re on the brink of giving up, or starting over, or starting out. And the only missing ingredient to your incredible success story in the future is a new and self-imposed discipline that will make you try harder and work more intensely than you ever thought you could.
The most valuable form of discipline is the one that you impose upon yourself. Don’t wait for things to deteriorate so drastically that someone else must impose discipline in your life. Wouldn’t that be tragic? How could you possibly explain the fact that someone else thought more of you than you thought of yourself? That they forced you to get up early and get out into the marketplace when you would have been content to let success go to someone else who cared more about themselves.
Your life, my life, the life of each one of us is going to serve as either a warning or an example. A warning of the consequences of neglect, self-pity, lack of direction and ambition… or an example of talent put to use, of discipline self-imposed, and of objectives clearly perceived and intensely pursued.
-What are your thoughts on the ideas above? What areas of your life can you improve in?
Success lesson
But first… A secret key to understanding success.
Secret Key: Success isn’t just doing certain things, though we will certainly do certain things to become a certain kind of person. What kind of person you are is what determines your success in life. Yes, you can do right things and achieve a certain level of success, but not the kind of success I am talking about – true life success.
So what are my four tips? Here the are:
1. Become a person of Vision…
Vision is the spectacular that causes us to carry out the mundane. Vision is what sees us through the dark days so we do not give up and settle for second best. Vision is the grand scheme that we relentlessly pursue. Vision is the goal we aim for. The best way to kick your life into high gear and begin to succeed in what you want to succeed in is to begin to become a person of vision.
The successful person has a fully developed vision of their destination. So let me ask you a simple question:
Do YOU know where you are going?
And not only do you have a vision of where you are going, but is your vision fully developed? Now certainly we cannot know everything that will happen to us in the future, but we can develop the plan fully, allowing in our plan for a variety of contingency plans. It is, but when you look across the board at people who have succeeded much, they are people who laid out most of their life and work before it happened. Life didn’t just happen to them. They didn’t just stumble into success. They planned for it and they created it.
The Tests of Vision
- Is it Clear?
- Is it Concise?
- Is it Inspiring?
- Is it Achievable?
- Is it Easy to Memorize?
Ask your self the questions above and let the answers begin to shape the vision you have for your life. The tighter and clearer the vision you have for your life, the sooner you will kick your life into high gear!
2. Become a person of Passion…
Passion. Mmmmm…. Passion. Passion is the burning of the heart. It is the unbridled running amuck of the emotions. It is the overwhelming desire to accomplish your goal. It transcends the mental assent to a set of ideals. It drives and thrusts you toward your goal. You MUST have it!
Those who consider themselves intellectuals will underestimate the power of passion. The fact is that the victory isn’t only in the mind. The truths of the mind are driven by the passion of the heart. So by all means, fuel the passion for life that resides deep within your soul.
Passion is like a fire. It can rage or it can smolder. Even if all you have is barely lit embers, you can fan into flame the fire of your passion for life, love, and the goals and vision you have for your life! Commit yourself to becoming a person who lives passionately!
3. Become a person of Priorities…
As I have worked through the years with people who achieve much and have lives that are constantly in high gear, I notice something amazing about them: They are people with an extraordinary ability to know what the right thing to do is and to actually do it in a timely fashion.
For example, a friend of mine was in charge of a three-day event that was attended by close to 250,000 people and was featured on national and international television. Four days before the event he told me he had nothing to do and felt guilty. I encouraged him by reminding him that this was actually a sign of his incredible ability to have focused on and lived out his priorities throughout the whole year before the event took place.
When all was said and done, living and working out of his priorities enabled him to kick back and enjoy the fruit of his (and hundreds of his employees) labor. His life was in high gear and because he is a person of priorities, he is enjoying life. You can too.
Discern what the important things are that you must involve yourself in so as to have the life you want. Then relentlessly live out of those priorities. Say “no” to everything else!
4. Become a person of Excellence…
People who live life in high gear, succeeding in every area of life, are people who place a high emphasis on and strive for excellence in every area of life. Good just won’t do. The best is the target.
Even when they fail or do poorly, they make an inner commitment to do an excellent job the next time. They are people who want, and live for, excellence in their work, their play, their finances, their relationships – everything!
Do you long for a life lived in high gear? One that is filled with joy and achievement? It is possible! Give some time to contemplate how you can make changes in the next few days and weeks in the following areas and see if your life doesn’t kick into high gear!
- Vision
- Passion
- Priorities
- Excellence
They are yours for the taking! Go get ‘em!
Secret Key: Success isn’t just doing certain things, though we will certainly do certain things to become a certain kind of person. What kind of person you are is what determines your success in life. Yes, you can do right things and achieve a certain level of success, but not the kind of success I am talking about – true life success.
So what are my four tips? Here the are:
1. Become a person of Vision…
Vision is the spectacular that causes us to carry out the mundane. Vision is what sees us through the dark days so we do not give up and settle for second best. Vision is the grand scheme that we relentlessly pursue. Vision is the goal we aim for. The best way to kick your life into high gear and begin to succeed in what you want to succeed in is to begin to become a person of vision.
The successful person has a fully developed vision of their destination. So let me ask you a simple question:
Do YOU know where you are going?
And not only do you have a vision of where you are going, but is your vision fully developed? Now certainly we cannot know everything that will happen to us in the future, but we can develop the plan fully, allowing in our plan for a variety of contingency plans. It is, but when you look across the board at people who have succeeded much, they are people who laid out most of their life and work before it happened. Life didn’t just happen to them. They didn’t just stumble into success. They planned for it and they created it.
The Tests of Vision
- Is it Clear?
- Is it Concise?
- Is it Inspiring?
- Is it Achievable?
- Is it Easy to Memorize?
Ask your self the questions above and let the answers begin to shape the vision you have for your life. The tighter and clearer the vision you have for your life, the sooner you will kick your life into high gear!
2. Become a person of Passion…
Passion. Mmmmm…. Passion. Passion is the burning of the heart. It is the unbridled running amuck of the emotions. It is the overwhelming desire to accomplish your goal. It transcends the mental assent to a set of ideals. It drives and thrusts you toward your goal. You MUST have it!
Those who consider themselves intellectuals will underestimate the power of passion. The fact is that the victory isn’t only in the mind. The truths of the mind are driven by the passion of the heart. So by all means, fuel the passion for life that resides deep within your soul.
Passion is like a fire. It can rage or it can smolder. Even if all you have is barely lit embers, you can fan into flame the fire of your passion for life, love, and the goals and vision you have for your life! Commit yourself to becoming a person who lives passionately!
3. Become a person of Priorities…
As I have worked through the years with people who achieve much and have lives that are constantly in high gear, I notice something amazing about them: They are people with an extraordinary ability to know what the right thing to do is and to actually do it in a timely fashion.
For example, a friend of mine was in charge of a three-day event that was attended by close to 250,000 people and was featured on national and international television. Four days before the event he told me he had nothing to do and felt guilty. I encouraged him by reminding him that this was actually a sign of his incredible ability to have focused on and lived out his priorities throughout the whole year before the event took place.
When all was said and done, living and working out of his priorities enabled him to kick back and enjoy the fruit of his (and hundreds of his employees) labor. His life was in high gear and because he is a person of priorities, he is enjoying life. You can too.
Discern what the important things are that you must involve yourself in so as to have the life you want. Then relentlessly live out of those priorities. Say “no” to everything else!
4. Become a person of Excellence…
People who live life in high gear, succeeding in every area of life, are people who place a high emphasis on and strive for excellence in every area of life. Good just won’t do. The best is the target.
Even when they fail or do poorly, they make an inner commitment to do an excellent job the next time. They are people who want, and live for, excellence in their work, their play, their finances, their relationships – everything!
Do you long for a life lived in high gear? One that is filled with joy and achievement? It is possible! Give some time to contemplate how you can make changes in the next few days and weeks in the following areas and see if your life doesn’t kick into high gear!
- Vision
- Passion
- Priorities
- Excellence
They are yours for the taking! Go get ‘em!
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