relativity-electromagnetism by AbdoAbdullahAbdo


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Maxwell’s theory for electromagnetism:
 Magnetism and electricity produce energy waves, which radiate in elds with differing wavelengths.

                                                     The most dramatic moments in the development of physics are
                                                     those in which great syntheses take place, where phenomena
                                                     which previousely had appeared to be different are suddenly
                                                     discovered to be but different aspects of the same thing. The
                                                     history of physics is the history of such syntheses, and the basis of
                                                     the success of physical science is mainly that we are able to
                                                         Perhaps the most dramatic moment in the development of
                                                     physics during the 19th century ocuured to J.C.Maxwell one day
                                                     in the 1860's, when he combined the laws of electricity and
                                                     magnetism with the laws of the behavior of light. As a result, the
                                                     properties of light were partly unravelled.
    Familiar with Michael Faraday’s theories of electricity and magnetic lines of force and expanding on the
mathematics developed by Faraday; Maxwell combined several equations that resulted in the establishment of direct
relationships in the elds produced by magnetism and electricity and how together they affect nature. Once the
equations for magnetic and electric elds were combined, he calculated the speed of their waves. Maxwell concluded
that electromagnetic radiation has the same speed as light—about 186,000 miles per second. At rst, Maxwell
accepted the ancient concept of the existence of the aether in space. (It was thought that light and other
electromagnetic waves could not travel in a vacuum; herefore the concept of ‘‘ethereal matter’’ in space was
invented but never veried.) Maxwell believed electromagnetic radiation waves were actually carried by this aether
and that magnetism caused disruptions to it.
Later, in 1887, Albert Michelson demonstrated that any material body such as aether in space was unnecessary for
the propagation of light. Maxwell’s equations were still valid, even after the aether concept was abandoned. Maxwell
concluded there were shorter wavelengths and longer wavelengths of electromagnetic radiation next to visible light
wavelengths on the electromagnetic spectrum (later named ultraviolet and infrared). He further concluded that
visible light was only a small portion of a ‘‘spectrum’’ of possible electromagnetic wavelengths. Maxwell then
speculated and predicted that electromagnetic radiation is composed of many different (both longer and shorter)
wavelengths of different frequencies. This concept developed into the electromagnetic spectrum, which ranges from
the very short wavelengths of cosmic and gamma radiation to the very long wavelengths of radio and electrical

                                                       The theory of electromagnetic radiation is one of the most
                                                     profound and important discoveries of our physical world. It has
                                                     aided our understanding of physical nature and resulted in many
                                                     technological developments, including radio, television, X-rays,
                                                     lighting, computers, iPods, cell phones, and electronic equipment.
                                                      Maxwell combined his four famous differential equations. These
                                                     four rather simple mathematical equations could be used to
                                                     describe interrelated nature and behavior of electric and magnetic
                                                     elds. They described the propagation of electromagnetic waves(
                                                     radiation) in a form of the wave equation. This was the rst time
the constant for the velocity of light waves (c) was used; it later became an important constant in Einstein’s theories
of relativity and his famous equation, E=mc².
Maxwell experimented in many areas, and his accomplishments were substantive, including an explanation of how
viscosity of a substance varies directly with its temperature. Maxwell’s contribution to the physical sciences was not
only signicant but his theories were among the few from his day in history that held up following the evolution in
knowledge that began with the advent of the new science of relativity by Albert Einstein.
   James Clerk Maxwell hypothesized the existence of electromagnetic radiation with longer and shorter wavelength
than visible light that is located near the middle of the scale. This idea developed into the electromagnetic radiation
spectrum for frequencies from very long radio waves to extremely short X-rays and cosmic radiation.
   Now, Consider two frames of reference S and S` that are in relative motion, and assume that a single charge q is at
rest in the S` frame of reference. According to an observer in this frame, an electric eld surrounds the charge.
However, an observer in frame S says that the charge is in motion and therefore measures both an electric eld and a
magnetic eld. The magnetic eld measured by the observer in frame S is created by the moving charge, which
constitutes an electric current.
In other words, electric and magnetic elds are viewed differently in frames of reference that are moving relative to
each other.
 We now describe one situation that shows how an electric eld in one frame of reference is viewed as a magnetic eld
in another frame of reference.

                                              A positive test charge q is moving parallel to a current-carrying wire with
                                              velocity v relative to the wire in frame S, as shown in Figure a. We
                                              assume that the net charge on the wire is zero and that the electrons in the
                                              wire also move with velocity v in a straight line. The leftward current in
                                              the wire produces a magnetic
                                              eld that forms circles around the wire and is directed into the page at the
                                              location of the moving test charge. Therefore, a magnetic force directed
                                              away from the wire is exerted on the test charge. However, no electric
                                              force acts on the test charge because the net charge on the wire is zero
                                              when viewed in this frame.
                                              Now consider the same situation as viewed from frame S`, where the test
                                              charge is at rest (Figure b). In this frame, the positive charges in the wire
                                              move to the left, the electrons in the wire are at rest, and the wire still
                                              carries a current. Because the test charge is not moving in this frame,
                                              there is no magnetic force exerted on the test charge when viewed in
                                              thisframe. However, if a force is exerted on the test charge in frameS`, the
                                              frame of the wire, as described earlier, a force must be exerted on it in
any other frame. What is the origin of this force in frame S, the frame of the test charge?
The answer to this question is provided by the special theory of relativity.
When the situation is viewed in frame S, as in Figure a, the positive charges are at rest and the electrons in the wire
move to the right with a velocity v. Because of length contraction, the electrons appear to be closer together than
their proper separation. Because there is no net charge on the wire this contracted separation
must equal the separation between the stationary positive charges. The situation is quite different when viewed in
frame S`, shown in Figure b. In this frame, the positive charges appear closer together because of length contraction,
and the electrons in the wire are at rest with a separation that is greater than that viewed in frame S. Therefore, there
is a net positive charge on the wire when viewed in frame S`. This net positive charge produces an electric eld
pointing away from the wire toward the test charge, and so the test charge experiences an electric force directed
away from the wire. Thus, what was viewed as a magnetic eld (and a corresponding magnetic force) in the frame of
the wire transforms into an electric eld (and a corresponding electric force) in the frame of the test charge.
for more details about Electricity and Magnetism see this video, I could not upload it :( Lec 22 | MIT 8.02
Electricity and Magnetism, Spring 2002

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