Under the photon theory of light, a photon is a discrete bundle (or quantum) of electromagnetic (or light) energy. Photons are always in motion and, in a vacuum, have a constant speed of light to all observers, at the vacuum speed of light (more commonly just called the speed of light) of c = 2.998 x 108 m/s.
Basic Properties of Photons
According to the photon theory of light, photons . . .
move at a constant velocity, c = 2.9979 x 108 m/s (i.e. "the speed of light"), in free space
have zero mass and rest energy.
carry energy and momentum, which are also related to the frequency nu and wavelength lamdba of the electromagnetic wave by E = h nu and p = h / lambda.
can be destroyed/created when radiation is absorbed/emitted.
can have particle-like interactions (i.e. collisions) with electrons and other particles, such as in the Compton effect.
History of Photons
The term photon was coined by Gilbert Lewis in 1926, though the concept of light in the form of discrete particles had been around for centuries and had been formalized in Newton's construction of the science of optics.
In the 1800s, however, the wave properties of light (by which I mean electromagnetic radiation in general) became glaringly obvious and scientists had essentially thrown the particle theory of light out the window. It wasn't until Albert Einstein explained the photoelectric effect and realized that light energy had to be quantized that the particle theory returned.
Wave-Particle Duality in Brief
As mentioned above, light has properties of both a wave and a particle. This was an astounding discovery and is certainly outside the realm of how we normally perceive things. Billiard balls act as particles, while oceans act as waves. Photons act as both a wave and a particle all the time (even though it's common, but basically incorrect, to say that it's "sometimes a wave and sometimes a particle" depending upon which features are more obvious at a given time).
Just one of the effects of this wave-particle duality (or particle-wave duality) is that photons, though treated as particles, can be calculated to have frequency, wavelength, amplitude, and other properties inherent in wave mechanics.
Fun Photon Facts
The photon is an elementary particle, despite the fact that it has no mass. It cannot decay on its own, although the energy of the photon can transfer (or be created) upon interaction with other particles. Photons are electrically neutral and are one of the rare particles that are identical to their antiparticle, the antiphoton.
Photons are spin-1 particles (making them bosons), with a spin axis that is parallel to the direction of travel (either forward or backward, depending on whether it's a "left-hand" or "right-hand" photon). This feature is what allows for polarization of light.
Friday, September 3, 2010
What is the Photoelectric Effect?
Though originally observed in 1839, the photoelectric effect was documented by Heinrich Hertz in 1887 in a paper to the Annalen der Physik. It was originally called the Hertz effect, in fact, though this name fell out of use.
When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right.
Setting Up the Photoelectric Effect
To observe the photoelectric effect, you create a vacuum chamber with the photoconductive metal at one end and a collector at the other. When a light shines on the metal, the electrons are released and move through the vacuum toward the collector. This creates a current in the wires connecting the two ends, which can be measured with an ammeter. (A basic example of the experiment can be seen by clicking on the image to the right, and then advancing to the second image available.)
By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation:
Kmax = eVs
It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.
The Classical Wave Explanation
In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is the work function phi of the material. (Phi is in the range of a few electron-volts for most common photoelectric materials.)
Three main predictions come from this classical explanation:
The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.
The photoelectric effect should occur for any light, regardless of frequency or wavelength.
There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
The Experimental Result
By 1902, the properties of the photoelectric effect were well documented. Experiment showed that:
The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons.
Below a certain frequency, the photoelectric effect does not occur at all.
There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
As you can tell, these three results are the exact opposite of the wave theory predictions. Not only that, but they are all three completely counter-intuitive. Why would low-frequency light not trigger the photoelectric effect, since it still carries energy? How do the photoelectrons release so quickly? And, perhaps most curiously, why does adding more intensity not result in more energetic electron releases? Why does the wave theory fail so utterly in this case, when it works so well in so many other situation Einstein's Wonderful Year
In 1905, Albert Einstein published four papers in the Annalen der Physik journal, each of which was significant enough to warrant a Nobel Prize in its own right. The first paper (and the only one to actually be recognized with a Nobel) was his explanation of the photoelectric effect.
Building on Max Planck's blackbody radiation theory, Einstein proposed that radiation energy is not continuously distributed over the wavefront, but is instead localized in small bundles (later called photons). The photon's energy would be associated with its frequency (nu), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (lambda) and the speed of light (c):
E = h nu = hc / lambda
or the momentum equation: p = h / lambda
In Einstein's theory, a photoelectron releases as a result of an interaction with a single photon, rather than an interaction with the wave as a whole. The energy from that photon transfers instantaneously to a single electron, knocking it free from the metal if the energy (which is, recall, proportional to the frequency nu) is high enough to overcome the work function (phi) of the metal. If the energy (or frequency) is too low, no electrons are knocked free.
If, however, there is excess energy, beyond phi, in the photon, the excess energy is converted into the kinetic energy of the electron:
Kmax = h nu - phi
Therefore, Einstein's theory predicts that the maximum kinetic energy is completely independent of the intensity of the light (because it doesn't show up in the equation anywhere). Shining twice as much light results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons won't change unless the energy, not the intensity, of the light changes.
The maximum kinetic energy results when the least-tightly-bound electrons break free, but what about the most-tightly-bound ones; The ones in which there is just enough energy in the photon to knock it loose, but the kinetic energy that results in zero? Setting Kmax equal to zero for this cutoff frequency (nuc), we get:
nuc = phi / h
or the cutoff wavelength: lambdac = hc / phi
These equations indicate why a low-frequency light source would be unable to free electrons from the metal, and thus would produce no photoelectrons.
After Einstein
Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, and his work confirmed Einstein's theory. Einstein won a Nobel Prize for his photon theory (as applied to the photoelectric effect) in 1921, and Millikan won a Nobel in 1923 (in part due to his photoelectric experiments).
Most significantly, the photoelectric effect, and the photon theory it inspired, crushed the classical wave theory of light. Though no one could deny that light behaved as a wave, after Einstein's first paper, it was undeniable that it was also a particle.
When a light source (or, more generally, electromagnetic radiation) is incident upon a metallic surface, the surface can emit electrons. Electrons emitted in this fashion are called photoelectrons (although they are still just electrons). This is depicted in the image to the right.
Setting Up the Photoelectric Effect
To observe the photoelectric effect, you create a vacuum chamber with the photoconductive metal at one end and a collector at the other. When a light shines on the metal, the electrons are released and move through the vacuum toward the collector. This creates a current in the wires connecting the two ends, which can be measured with an ammeter. (A basic example of the experiment can be seen by clicking on the image to the right, and then advancing to the second image available.)
By administering a negative voltage potential (the black box in the picture) to the collector, it takes more energy for the electrons to complete the journey and initiate the current. The point at which no electrons make it to the collector is called the stopping potential Vs, and can be used to determine the maximum kinetic energy Kmax of the electrons (which have electronic charge e) by using the following equation:
Kmax = eVs
It is significant to note that not all of the electrons will have this energy, but will be emitted with a range of energies based upon the properties of the metal being used. The above equation allows us to calculate the maximum kinetic energy or, in other words, the energy of the particles knocked free of the metal surface with the greatest speed, which will be the trait that is most useful in the rest of this analysis.
The Classical Wave Explanation
In classical wave theory, the energy of electromagnetic radiation is carried within the wave itself. As the electromagnetic wave (of intensity I) collides with the surface, the electron absorbs the energy from the wave until it exceeds the binding energy, releasing the electron from the metal. The minimum energy needed to remove the electron is the work function phi of the material. (Phi is in the range of a few electron-volts for most common photoelectric materials.)
Three main predictions come from this classical explanation:
The intensity of the radiation should have a proportional relationship with the resulting maximum kinetic energy.
The photoelectric effect should occur for any light, regardless of frequency or wavelength.
There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons.
The Experimental Result
By 1902, the properties of the photoelectric effect were well documented. Experiment showed that:
The intensity of the light source had no effect on the maximum kinetic energy of the photoelectrons.
Below a certain frequency, the photoelectric effect does not occur at all.
There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.
As you can tell, these three results are the exact opposite of the wave theory predictions. Not only that, but they are all three completely counter-intuitive. Why would low-frequency light not trigger the photoelectric effect, since it still carries energy? How do the photoelectrons release so quickly? And, perhaps most curiously, why does adding more intensity not result in more energetic electron releases? Why does the wave theory fail so utterly in this case, when it works so well in so many other situation Einstein's Wonderful Year
In 1905, Albert Einstein published four papers in the Annalen der Physik journal, each of which was significant enough to warrant a Nobel Prize in its own right. The first paper (and the only one to actually be recognized with a Nobel) was his explanation of the photoelectric effect.
Building on Max Planck's blackbody radiation theory, Einstein proposed that radiation energy is not continuously distributed over the wavefront, but is instead localized in small bundles (later called photons). The photon's energy would be associated with its frequency (nu), through a proportionality constant known as Planck's constant (h), or alternately, using the wavelength (lambda) and the speed of light (c):
E = h nu = hc / lambda
or the momentum equation: p = h / lambda
In Einstein's theory, a photoelectron releases as a result of an interaction with a single photon, rather than an interaction with the wave as a whole. The energy from that photon transfers instantaneously to a single electron, knocking it free from the metal if the energy (which is, recall, proportional to the frequency nu) is high enough to overcome the work function (phi) of the metal. If the energy (or frequency) is too low, no electrons are knocked free.
If, however, there is excess energy, beyond phi, in the photon, the excess energy is converted into the kinetic energy of the electron:
Kmax = h nu - phi
Therefore, Einstein's theory predicts that the maximum kinetic energy is completely independent of the intensity of the light (because it doesn't show up in the equation anywhere). Shining twice as much light results in twice as many photons, and more electrons releasing, but the maximum kinetic energy of those individual electrons won't change unless the energy, not the intensity, of the light changes.
The maximum kinetic energy results when the least-tightly-bound electrons break free, but what about the most-tightly-bound ones; The ones in which there is just enough energy in the photon to knock it loose, but the kinetic energy that results in zero? Setting Kmax equal to zero for this cutoff frequency (nuc), we get:
nuc = phi / h
or the cutoff wavelength: lambdac = hc / phi
These equations indicate why a low-frequency light source would be unable to free electrons from the metal, and thus would produce no photoelectrons.
After Einstein
Experimentation in the photoelectric effect was carried out extensively by Robert Millikan in 1915, and his work confirmed Einstein's theory. Einstein won a Nobel Prize for his photon theory (as applied to the photoelectric effect) in 1921, and Millikan won a Nobel in 1923 (in part due to his photoelectric experiments).
Most significantly, the photoelectric effect, and the photon theory it inspired, crushed the classical wave theory of light. Though no one could deny that light behaved as a wave, after Einstein's first paper, it was undeniable that it was also a particle.
Albert Einstein - Biography
Nationality: German
Born: March 14, 1879
Death: April 18, 1955
Spouse:
Mileva Maric (1903 - 1919)
Elsa Lowenthal (1919 - 1936)
1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" (from the official Nobel Prize announcement)
Albert Einstein - Early Work:
In 1901, Albert Einstein received his diploma as a teacher of physics and mathematics. Unable to find a teaching position, he went to work for the Swiss Patent Office. He obtained his doctoral degree in 1905, the same year he published four significant papers, introducing the concepts of special relativity and the photon theory of light.
Albert Einstein & Scientific Revolution:
Albert Einstein's work in 1905 shook the world of physics. In his explanation of the photoelectric effect he introduced the photon theory of light. In his paper "On the Electrodynamics of Moving Bodies," he introduced the concepts of special relativity.
Einstein spent the rest of his life and career dealing with the consequences of these concepts, both by developing general relativity and by questioning the field of quantum physics on the principle that it was "spooky action at a distance."
Albert Einstein Moves to America:
In 1933, Albert Einstein renounced his German citizenship and moved to America, where he took a post at the Institute for Advanced Study in Princeton, New Jersey, as a Professor of Theoretical Physics. He gained American citizenship in 1940.
He was offered the first presidency of Israel, but he declined it, though he did help found the Hebrew University of Jerusalem.
Misconceptions About Albert Einstein:
The rumor began circulating even while Albert Einstein was alive that he had failed mathematics courses as a child. While it is true that Einstein began to talk late - at about age 4 according to his own accounts - he never failed in mathematics, nor did he do poorly in school in general. He did fairly well in his mathematics courses throughout his education and briefly considered becoming a mathematician. He recognized early on that his gift was not in pure mathematics, a fact he lamented throughout his career as he sought out more accomplished mathematicians to assist in the formal descriptions of his theories.
Born: March 14, 1879
Death: April 18, 1955
Spouse:
Mileva Maric (1903 - 1919)
Elsa Lowenthal (1919 - 1936)
1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect" (from the official Nobel Prize announcement)
Albert Einstein - Early Work:
In 1901, Albert Einstein received his diploma as a teacher of physics and mathematics. Unable to find a teaching position, he went to work for the Swiss Patent Office. He obtained his doctoral degree in 1905, the same year he published four significant papers, introducing the concepts of special relativity and the photon theory of light.
Albert Einstein & Scientific Revolution:
Albert Einstein's work in 1905 shook the world of physics. In his explanation of the photoelectric effect he introduced the photon theory of light. In his paper "On the Electrodynamics of Moving Bodies," he introduced the concepts of special relativity.
Einstein spent the rest of his life and career dealing with the consequences of these concepts, both by developing general relativity and by questioning the field of quantum physics on the principle that it was "spooky action at a distance."
Albert Einstein Moves to America:
In 1933, Albert Einstein renounced his German citizenship and moved to America, where he took a post at the Institute for Advanced Study in Princeton, New Jersey, as a Professor of Theoretical Physics. He gained American citizenship in 1940.
He was offered the first presidency of Israel, but he declined it, though he did help found the Hebrew University of Jerusalem.
Misconceptions About Albert Einstein:
The rumor began circulating even while Albert Einstein was alive that he had failed mathematics courses as a child. While it is true that Einstein began to talk late - at about age 4 according to his own accounts - he never failed in mathematics, nor did he do poorly in school in general. He did fairly well in his mathematics courses throughout his education and briefly considered becoming a mathematician. He recognized early on that his gift was not in pure mathematics, a fact he lamented throughout his career as he sought out more accomplished mathematicians to assist in the formal descriptions of his theories.
Thursday, September 2, 2010
What Is Quantum Physics?:
Quantum physics is the study of the behavior of matter and energy at the molecular, atomic, nuclear, and even smaller microscopic levels. In the early 20th century, it was discovered that the laws that govern macroscopic objects do not function the same in such small realms.
What Does Quantum Mean?:
"Quantum" comes from the Latin meaning "how much." It refers to the discrete units of matter and energy that are predicted by and observed in quantum physics. Even space and time, which appear to be extremely continuous, have smallest possible values.
Who Developed Quantum Mechanics?:
As scientists gained the technology to measure with greater precision, strange phenomena was observed. The birth of quantum physics is attributed to Max Planck's 1900 paper on blackbody radiation. Development of the field was done by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schroedinger, and many others. Ironically, Albert Einstein had serious theoretical issues with quantum mechanics and tried for many years to disprove or modify it.
What's Special About Quantum Physics?:
In the realm of quantum physics, observing something actually influences the physical processes taking place. Light waves act like particles and particles act like waves (called wave particle duality). Matter can go from one spot to another without moving through the intervening space (called quantum tunnelling). Information moves instantly across vast distances. In fact, in quantum mechanics we discover that the entire universe is actually a series of probabilities. Fortunately, it breaks down when dealing with large objects, as demonstrated by the Schroedinger's Cat thought experiment.
Quantum Optics:
Quantum optics is a branch of quantum physics that focuses primarily on the behavior of light, or photons. At the level of quantum optics, the behavior of individual photons has a bearing on the outcoming light, as opposed to classical optics, which was developed by Sir Isaac Newton. Lasers are one application that has come out of the study of quantum optics.
Quantum Electrodynamics (QED):
Quantum electrodynamics (QED) is the study of how electrons and photons interact. It was developed in the late 1940s by Richard Feynman, Julian Schwinger, Sinitro Tomonage, and others. The predictions of QED regarding the scattering of photons and electrons are accurate to eleven decimal places.
What Does Quantum Mean?:
"Quantum" comes from the Latin meaning "how much." It refers to the discrete units of matter and energy that are predicted by and observed in quantum physics. Even space and time, which appear to be extremely continuous, have smallest possible values.
Who Developed Quantum Mechanics?:
As scientists gained the technology to measure with greater precision, strange phenomena was observed. The birth of quantum physics is attributed to Max Planck's 1900 paper on blackbody radiation. Development of the field was done by Max Planck, Albert Einstein, Niels Bohr, Werner Heisenberg, Erwin Schroedinger, and many others. Ironically, Albert Einstein had serious theoretical issues with quantum mechanics and tried for many years to disprove or modify it.
What's Special About Quantum Physics?:
In the realm of quantum physics, observing something actually influences the physical processes taking place. Light waves act like particles and particles act like waves (called wave particle duality). Matter can go from one spot to another without moving through the intervening space (called quantum tunnelling). Information moves instantly across vast distances. In fact, in quantum mechanics we discover that the entire universe is actually a series of probabilities. Fortunately, it breaks down when dealing with large objects, as demonstrated by the Schroedinger's Cat thought experiment.
Quantum Optics:
Quantum optics is a branch of quantum physics that focuses primarily on the behavior of light, or photons. At the level of quantum optics, the behavior of individual photons has a bearing on the outcoming light, as opposed to classical optics, which was developed by Sir Isaac Newton. Lasers are one application that has come out of the study of quantum optics.
Quantum Electrodynamics (QED):
Quantum electrodynamics (QED) is the study of how electrons and photons interact. It was developed in the late 1940s by Richard Feynman, Julian Schwinger, Sinitro Tomonage, and others. The predictions of QED regarding the scattering of photons and electrons are accurate to eleven decimal places.
What Is Physics?
Physics is the scientific study of matter and energy and how they interact with each other.
This energy can take the form of motion, light, electricity, radiation, gravity . . . just about anything, honestly. Physics deals with matter on scales ranging from sub-atomic particles (i.e. the particles that make up the atom and the particles that make up those particles) to stars and even entire galaxies. How Physics Works
As an experimental science, physics utilizes the scientific method to formulate and test hypotheses that are based on observation of the natural world. The goal of physics is to use the results of these experiments to formulate scientific laws, usually expressed in the language of mathematics, which can then be used to predict other phenomena.
The Role of Physics in Science
In a broader sense, physics can be seen as the most fundamental of the natural sciences. Chemistry, for example, can be viewed as a complex application of physics, as it focuses on the interaction of energy and matter in chemical systems. We also know that biology is, at its heart, an application of chemical properties in living things, which means that it is also, ultimately, ruled by the physical laws.
This energy can take the form of motion, light, electricity, radiation, gravity . . . just about anything, honestly. Physics deals with matter on scales ranging from sub-atomic particles (i.e. the particles that make up the atom and the particles that make up those particles) to stars and even entire galaxies. How Physics Works
As an experimental science, physics utilizes the scientific method to formulate and test hypotheses that are based on observation of the natural world. The goal of physics is to use the results of these experiments to formulate scientific laws, usually expressed in the language of mathematics, which can then be used to predict other phenomena.
The Role of Physics in Science
In a broader sense, physics can be seen as the most fundamental of the natural sciences. Chemistry, for example, can be viewed as a complex application of physics, as it focuses on the interaction of energy and matter in chemical systems. We also know that biology is, at its heart, an application of chemical properties in living things, which means that it is also, ultimately, ruled by the physical laws.
Wednesday, September 1, 2010
An expandable molecular sponge
Zinc ions and some other metal ions can bind to three or four organic molecules at once. If those molecules are long and attach to zinc at both ends, it's possible to create a metal–organic framework (MOF), an open sheet of linked molecules with ions at the vertices. And if those sheets bind to each other and stack in register, the result is a material whose columnar pores can store, catalyze, or otherwise usefully process small molecules. Matthew Rosseinsky and his coworkers at the University of Liverpool in the UK have made a MOF material, but with a new twist. For its linker, the Liverpool team used a dipeptide—that is, two peptide-bonded amino acids (glycine and alanine; see figure). The team made two versions of the material, one incorporating a solvent (a mix of water and methanol) and one not. X-ray diffraction and nuclear magnetic resonance spectroscopy revealed that adding the solvent caused the dipeptide linkers to straighten, widening the pores to accommodate the solvent ions. Glycine, alanine, and the 18 other naturally occurring amino acids are characterized by side chains that are polar, nonpolar, positively charged, or negatively charged. Given that variety, the Liverpool experiment suggests that peptide-based MOF materials might find uses as expandable sponges for a wide range of molecules.
Tuesday, August 31, 2010
Electromagnetic Induction
Introduction
Ørsted had discovered that electricity and magnetism were linked, electric current gave rise to magnetic fields. However no one had succeded in generating electricity by using magnetic fields, until Michael Faraday found that moving a conductor in a magnetic field (or by moving the magnet field near a stationary conductor) created a voltage. The wire must be part of an electrical circuit. Otherwise the electrons have no place to go. In other words, there is no electrical current produced with a wire with open ends. But if the ends are attached to a light bulb, to an electrical meter or even to each other, the circuit is complete and electrical current is created.
Figure 1. Inducing a current in a wire by moving the wire in a magnetic field.
Direction of Current
The direction of the current is determined by Flemming's Right hand rule. The left-hand rule is used for motors and motion produced by a magnetic field. The right-hand rule is used for generators and current generated by a motion. Using the right-hand, the thumb is in the direction of the motion, the first finger points in the direction of the field and the second finger points in the direction of the current.
Flux and Flux Linkage
To create electricity all that was required was a coil of wire, ends of which may be connected to a voltmeter. The voltage created depends on the density of the magnetic field and the area of the loop cutting the magnetic field lines.
A quantity called the flux measures this and is give by &phi = BA where B is the magnetic flux density and A is the area of the coil in the magnetic field.
If there are more turns in the coil then the flux is termed the magnetic flux linkage. It is given by Nφ =BAN. This assumes that the loop cuts the magnetic field lines at an angle of 90°. If the loop cuts the magnetic field lines at a different angle say, θ then the flux linkage is defined as N&phi = BANcos θ where theta is the angle by the normal to the area and the magnetic field lines as shown in Figure 1.
Faraday's Law of Induction
We said that a voltage or Electro-Motive Force (EMF), is produced when the loop is moved in the magnetic field but more qualitatively, the voltage is produced is in responce to the change in the motion. The voltage produced depends on the rate of change of flux-linkage with time. In mathematical terms,
where E is the EMF. The other symbols have their usual meanings. The minus sign is a consequence of Lenz's Law which we shall discuss in the following section.
Lenz's Law
When we move a conductor in a magnetic field the current generated creates it's own magnetic field. If the magnetic field created had an additive effect to the original magnetic field then the magnetic field would become even stronger and this would create an even stronger current which would create an even strong magnetic field, and so on. If this were to happen we could get energy for free although the universe might explode. Unfortunately we cannot make free energy the reason is down to the Lenz's law. When a current is generated, the magnetic field produced by the current is in opposition to the original magnetic field. This produces a force opposes the motion of the conductor and brings it to a halt. This is why it becomes more difficult to turn a dynamo on a bicycle as you increase in speed. We express Lenz's law in as part of Faraday's Law by inserting a minus sign.
Ørsted had discovered that electricity and magnetism were linked, electric current gave rise to magnetic fields. However no one had succeded in generating electricity by using magnetic fields, until Michael Faraday found that moving a conductor in a magnetic field (or by moving the magnet field near a stationary conductor) created a voltage. The wire must be part of an electrical circuit. Otherwise the electrons have no place to go. In other words, there is no electrical current produced with a wire with open ends. But if the ends are attached to a light bulb, to an electrical meter or even to each other, the circuit is complete and electrical current is created.
Figure 1. Inducing a current in a wire by moving the wire in a magnetic field.
Direction of Current
The direction of the current is determined by Flemming's Right hand rule. The left-hand rule is used for motors and motion produced by a magnetic field. The right-hand rule is used for generators and current generated by a motion. Using the right-hand, the thumb is in the direction of the motion, the first finger points in the direction of the field and the second finger points in the direction of the current.
Flux and Flux Linkage
To create electricity all that was required was a coil of wire, ends of which may be connected to a voltmeter. The voltage created depends on the density of the magnetic field and the area of the loop cutting the magnetic field lines.
A quantity called the flux measures this and is give by &phi = BA where B is the magnetic flux density and A is the area of the coil in the magnetic field.
If there are more turns in the coil then the flux is termed the magnetic flux linkage. It is given by Nφ =BAN. This assumes that the loop cuts the magnetic field lines at an angle of 90°. If the loop cuts the magnetic field lines at a different angle say, θ then the flux linkage is defined as N&phi = BANcos θ where theta is the angle by the normal to the area and the magnetic field lines as shown in Figure 1.
Faraday's Law of Induction
We said that a voltage or Electro-Motive Force (EMF), is produced when the loop is moved in the magnetic field but more qualitatively, the voltage is produced is in responce to the change in the motion. The voltage produced depends on the rate of change of flux-linkage with time. In mathematical terms,
where E is the EMF. The other symbols have their usual meanings. The minus sign is a consequence of Lenz's Law which we shall discuss in the following section.
Lenz's Law
When we move a conductor in a magnetic field the current generated creates it's own magnetic field. If the magnetic field created had an additive effect to the original magnetic field then the magnetic field would become even stronger and this would create an even stronger current which would create an even strong magnetic field, and so on. If this were to happen we could get energy for free although the universe might explode. Unfortunately we cannot make free energy the reason is down to the Lenz's law. When a current is generated, the magnetic field produced by the current is in opposition to the original magnetic field. This produces a force opposes the motion of the conductor and brings it to a halt. This is why it becomes more difficult to turn a dynamo on a bicycle as you increase in speed. We express Lenz's law in as part of Faraday's Law by inserting a minus sign.
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