James C. Maxwell: Lecture Notes (Electric & Magnetic Fields in Space) - Maxwell (1831-1879) was a Scottish physicist who is generally regarded as the most profound and productive physicist between the time of Newton and Einstein - he organized the Cavendish Laboratory at Cambridge University, which soon became a world center for physics research - he was one of the main contributors to the kinetic theory of gases, to statistical mechanics and thermodynamics, and also the theory of color vision; his greatest achievement was his electromagnetic theory - he is generally regarded as the most profound and productive physicist between the time of Newton and Einstein Principles of Electromagnetism: - in the 1860's, when Maxwell began his work on electromagnetism, there were two basic principles established by Oersted, Ampere, Henry, and Faraday - the two principles of electromagnetism were: 1) An electric current in a conductor produces magnetic lines of force that circle the conductor 2) When a conductor moves across externally set-up magnetic lines of force, a current is induced in the conductor - Maxwell added to and generalized these principles so that they applied to electric and magnetic fields in conductors, insulators, and in space free of matter
- Maxwell described an entirely new idea that had far-reaching consequences: an electric field that is changing with time must be accompanied by a magnetic field - not only do steady electric currents passing through conductors (conduction currents) produce magnetic fields around the conductors, but also changing electric fields insulators such as air, glass, or even space produce magnetic fields Clearing Up Maxwell's New Idea: - uncharged insulators contain equal amounts of positive and negative charge; in the normal state, these charges are distributed evenly - as a result of these charges being evenly distributed, the net charge is zero in every region of the material - but when the insulator is placed in an electric field, these charges are subjected to electrical forces; the positive charges are pushed in one direction and the negative charges in the opposite direction - unlike charges in a conductor, the charges in an insulating material are not free to move far through the material; instead, the charges can be displaced only a small distance before restoring forces in the insulator balance the force of the electric field - if the strength of the electric field increases, then the particles will be displaced further
- the changing displacement of charges that accompanies a changing electric field in an insulator briefly forms a current - Maxwell called this displacement current; and he assumed that the displacement current surrounds itself with a magnetic field just as a conduction current does - in an insulator, the displacement current is defined as the rate at which the charge displacement changes; this rate is directly proportional to the rate at which the electric field is changing in time - therefore, the magnetic field that circles the displacement current is a consequence of the electric field changing over time - previously, it was thought that the only current that produced a magnetic field was the current in a conductor; now Maxwell predicted that a magnetic field would also arise from a changing electric field (even in empty space) - now we can add a third principle to the other two principles of electromagnetism: 3) A changing electric field in space produces a magnetic field - the induced magnetic field vector B is in a plane perpendicular to the changing electric field vector E - the magnitude of B depends on the rate at which E is changing, not on E itself, but on ΔE/Δt - the higher the rate of alteration of E the greater the field B so induced - an additional principle known before Maxwell assumed new significance in Maxwell's work because it is symmetrical to principle 3 above: 4) A changing magnetic field in space produces an electric field
- the induced electric field vector E is in a plane perpendicular to the changing magnetic field vector B - similarly to principle 3, the magnitude of E depends on the rate at which B is changing, not on B itself but on ΔB/Δt
Propagation of EM Waves: - suppose somewhere in space an electric field is created that changes with time; according to Maxwell's theory, an electric field E that varies in time simultaneously induces a magnetic field B that also varies with time - the strength of the magnetic field also varies with the distance from the region where the changing electric field was created - similarly, a magnetic field that is changing with time simultaneously induces an electric field that changes with time - here too, the strength of the electric field also change with distance from the region where the changing magnetic field was created - the electric and magnetic field changes occur together, much like the "action" and "reaction" of Newton's third law - as Maxwell predicted, the mutual induction of varying electric and magnetic fields should set up an unending sequence of events 1) a time-varying E in one region produces a time-varying and space-varying B at points near this region 2) this B produces a time and space-varying E in the space surrounding it 3) and this E produces time and space-varying B in its neighborhood, and so on - thus, suppose that an EM disturbance is started at a location in space, say by vibrating charges in a hot gas or in the transmitter wire of a television station; this disturbance can travel to distant points through the mutual generation of the E and B
- the fluctuating, interlocked electric and magnetic fields propagate through space as a wave; this type of wave is called an electromagnetic wave - in the first semester, we studied mechanical waves, such as those we created in springs and the Slinky - we saw that waves occur when a disturbance created in one region produces at a later time, a disturbance in adjacent regions - analogously, time-varying E and B produce a disturbance that moves away from the source as the varying fields in one region create varying fields in neighboring regions The Speed of EM Waves: - Maxwell calculated the speed of EM waves to be about 311,000,000 m/s - he was immediately struck by the fact that this was a large number which was very close to the speed of light (now known to be 299,792,458 m/s) - Maxwell believed that there must be a deep underlying reason for these two numbers being so nearly the same
- at this time it was already known that light was a transverse wave; when Maxwell found that the E and B were perpendicular to each other and to the direction of propagation of the wave, he concluded that EM waves are also transverse - Maxwell provided a new synthesis; that light waves as well as EM waves were both transverse and traveled at the same speed - just as physics flourished after Newton published his ideas on mechanics in the late 1600's; so too did it during the late 1800's with Maxwell's electromagnetic theory - theoretically, Maxwell's EM theory led to a new way of looking at natural phenomena; not only was the universe a Newtonian machine of whirling and colliding parts; but it also included fields and energies that no machine could duplicate; it also formed the basis for Einstein's theory of relativity - practically, Maxwell's ideas led directly to the discovery of the radio and television - the physics of the everyday, visible world, based upon the ideas of Newton and Maxwell are often called classical physics - eventually, however, as research pushed into unfamiliar realms of nature at the scale of the very small (inside atoms), the very fast (approaching the speed of light), and the very large (the size of the universe), results accumulated that could not be explained using classical physics - something new was needed; starting about 1925, the development of quantum mechanics led to a new synthesis which included Maxwell's electromagnetism theory
Hertz's Experimental Confirmation: - Maxwell did not actually establish that light consists of em waves or even that em waves exist at all; in fact, most scientists remained skeptical for several years - Maxwell provided data which suggested that some connection between electricity and light existed, but stronger evidence was still needed - experimental evidence which supported Maxwell's ideas was conducted by Heinrich Hertz in 1888 - Hertz's experiments would verify Maxwell's predictions that em waves of many different frequencies could exist and all such waves would propagate through space at the speed of light - Hertz invented an apparatus that could both produce and detect em waves
- this device studied an effect that was triggered by a chance observation - in 1886, Hertz noticed an unusual effect produced during the sparking of an induction coil - it was already known at this time that sparks sometimes jump the air gap between the terminals of an induction coil - an induction coil can produce high voltages if there are many more turns of wire on one side than on the other - this high voltage causes a visible spark to form; Hertz controlled the frequency of these sparks by changing the shape and size of the terminals
- the unusual effect Hertz noticed was that a spark of equal frequency to that created by the induction coil was created on a bent piece of wire if held near the induction coil - the wire was bent in such a way so that there was a short gap between its two ends - Hertz reasoned that as the spark oscillates across the gap of the induction coil, it must set up rapidly changing electric and magnetic fields - according to Maxwell's em theory, these changing E and B would propagate through space as em waves - the frequency of the em waves would be the same as the frequency of the sparks in the induction coil - when the propagating em wave created by the induction coil hit the bent wire (detector), they set up rapidly changing E and B there, too - the strong E in the detector created a spark in its air gap as well - Hertz's observation of the induced spark in the detector was the first experimental evidence that em waves exist - Hertz performed experiments on these em waves to see if they followed the same principles as other waves, such as reflection, refraction, diffraction, interference, and polarization - em waves were found by Hertz to obey all of these principles - Hertz also determined experimentally that em waves travel at the speed of light
The Electromagnetic Spectrum: - Hertz's induction coil produced em radiation with a wavelength of about 1 meter, which is about one million times the wavelength of visible light - experiments showed that a wide and continuous range of em wavelengths and frequencies is possible; the entire range is called the electromagnetic spectrum - this is not to be confused with the visible spectrum, which includes only the frequencies of visible light - the em spectrum theoretically ranges from close to 0 Hz - Hz, but in practice ranges from 1 Hz - 10 26 Hz; this corresponds to wavelength from 10 8 m - 10-18 m - special names are given to certain regions of the em spectrum; you can see these in the diagram below - in each of these regions, radiation is produced or observed in a particular way Ex. visible light is detected directly through its effect on the retina of the eye whereas radio waves can only be detected through electronic equipment
- the named regions may overlap Ex. some radiation is called UV or X-ray depending on where it lies on the total spectrum or how it is produced - all em waves, although they may be produced and detected in various ways, behave as Maxwell predicted 1) they all travel at the speed of light in empty space (3 10 8 m/s) 2) they all carry energy; when they are absorbed, the absorber is heated Ex. food in a microwave oven 3) em waves can only be emitted if energy is supplied to the source of radiation 4) the source of em waves is a charge undergoing acceleration Ex. heating a material will increase the vibrational energy of a charge 5) the motion of the accelerating charge on an electric conductor (antenna) can be changed Regions of the EM Spectrum: I. Radio Waves (λ = 10 m - 10,000m; f = 10 4 Hz - 10 7 Hz) - em waves in this region are reflected well by the electrically charged layers of ions that exist in the upper atmosphere (ionosphere) - this makes it possible to detect radio waves at great distances from the source
- because of their long wavelengths, radio waves can easily diffract around relatively small obstacles like trees or buildings; large objects such as hills and mountains may cast "dark" shadows - radio waves are useful for carrying information because they can travel long distances (either directly or by relay) - in 1901, Guglielmo Marconi successfully detected radio waves sent from Newfoundland to Ireland (first trans- Atlantic radio signal) II. Television, FM, and Radar (λ = about 1 m; f = 10 8 Hz) - waves at high frequencies of about 10 8 Hz or greater are not reflected by the layers of electric charge in the upper atmosphere - rather, the signals travel in nearly straight lines and pass into space; thus, they can be used in communication between the Earth and orbiting satellites - on the Earth's surface, TV signals cannot be received directly between points more than about 80 km apart, even if there are no mountains in the way; this is due to the curvature of the Earth's surface) - instead, communications satellites are used to relay signals either directly to the receiver in a home equipped with a satellite dish, or to a cable-company receiver, which then relays the signal to its customers over a large region using cables - signals at wavelengths of about 1 m are not diffracted much around objects that have dimensions of several meters, (cars, ships, or aircraft) so the reflected portions of signals of this length can be used to detect these objects
- pulses at around 1 m are sent out and hit the object which you are trying to detect; a device then measures the time between the emission of a pulse and the reception of its echo; this technique is called "radio detection and ranging" or radar III. Microwave (λ = 10-1 m - 10-4 m; f = 10 9 Hz - 10 12 Hz) - em waves in this region also do not bounce off the ionosphere, but instead pass easily through it - these waves are used for communicating with devices far beyond the Earth's atmosphere, such as those sent to explore space - microwave radiation interacts strongly with the charged particles in ordinary matter - this behavior is used in microwave ovens, in which the kinetic energy of the oscillating charges in food appears as heat, warming the food very quickly - microwaves can damage living tissue IV. Infrared (λ = 10-4 m - 10-6 m; f = 10 12 Hz - 10 14 Hz) - radiation in this region of the em spectrum is just below the red end of the visible spectrum - it is often called "thermal radiation" because it transmits heat
- because of the oscillation of charges within molecules due to heat energy, all warm objects emit infrared em waves - infrared rays are used by the Sun to transmit heat to the Earth - global warming is associated with infrared radiation - since the Earth is warmed by the Sun, our planet emits infrared rays; much of this radiation is dissipated into space - some of these rays are naturally trapped by water vapor in our atmosphere; this is called the greenhouse effect since greenhouses operate in a similar way - due to increases in fossil fuel consumption, which produces carbon dioxide, sulfur dioxide, water vapor and other gases, more infrared radiation emitted by the Earth is becoming trapped in the atmosphere and may lead to global warming
V. Visible Light (λ = 7 10-7 m to 4 10-7 m; f = 4 10 14 Hz to 8 10 14 Hz) - this small band of frequencies is known as visible light because the visual receptors in the human eye are sensitive to only these frequencies - the various frequencies correspond to different colors; which can be viewed when white light is sent through a glass prism - these colors range from red at the low-frequency end, 4 10 14 Hz to violet at the high-frequency end 8 10 14 Hz - the visible light frequencies are those at which the Sun copiously radiates energy; this is why over the course of evolution, the human eye has taken advantage of light in this region VI. Ultraviolet (λ about 10-7 m - 10-8 m; f about 10 15 Hz - 10 16 Hz) - em waves above the visible light region can damage living tissue; some can cause cancer and genetic mutations - the Sun emits UV radiation; but fortunately for us, the Earth's atmosphere provides some protection - our atmosphere blocks UV rays with a layer containing a molecule called ozone (a rare form of oxygen, O 3 ) - ozone vibrates at the same frequency as UV rays and can therefore absorb or reflect these rays back into space - man-made chemicals known as CFC's (chlorofluorocarbons) have been destroying the ozone layer since the 1930's
- CFC's were once widely used as refrigerants and propellant in aerosols, but are banned today VII. X rays (λ = 10-8 m to 10-17 m; f = 10 16 Hz to 10 25 Hz) - atoms emit X radiation when electrons undergo transitions between the inner shells of the atoms - X rays are also produced by the sudden deflection or stopping of electrons when they strike a metal target - X rays are readily absorbed by bone, while they pass through less dense organic matter such as flesh - these properties combined with their ability to affect a photographic plate have led to some spectacular medical uses of X ray photography VIII. Gamma rays (λ = 10-17 m and smaller; f = 10 25 Hz and higher) - the gamma-ray region of the em spectrum overlaps the X ray region - gamma rays are emitted by the unstable nuclei of natural or artificial radioactive materials - they are also a component of cosmic radiation (radiation streaming to the Earth from outer space)
- gamma rays are the most energetic radiation known; they are produced by the most energy intensive events in the universe (supernovae explosions and other cataclysmic events)