Larmor's Equation ```Name: Joe Status: student Age: N/A Location: N/A Country: N/A Date: N/A ``` Question: I have a simple question and I have tried to find the answer in reference texts and your library, but have failed. Here is my question: I know that accelerating electrons generate electromagnetic radiation because of the changes in the static electric field. I have seen that solution online. I believe it is called Larmor's equation. However, electrons have both static electric and magnetic fields. So, does an electron emit electro-magnetic radiation when it is moving at a constant velocity, and in a straight line? Both of these fields are changing but not like in the case of particle acceleration. The two fields appear to be independent of each other caused by different mechanisms. I have not seen that case addressed in my textbooks and have not found a discussion on line. I seems like this problem has a simple answer, but I am struggling with the concepts of Maxwell's equations. Replies: Joe First of all AC vs DC. Direct Current (DC) is a flow of charges (current-amperes) that flows in one direction. Here the charges are flowing in a "Static" electric field. Alternating Current (AC) is a flow of current first in one direction, then in the other direction such that you can measure the change in direction as a frequency (cycles per second - Hertz (Hz)). Here the charges are flowing back and forth establishing a "Dynamic" Electric field. When charged particles move down a wire (a current), a magnetic field is generated. If it is a DC current, a magnetic field of constant magnitude develops, if it is an AC current, the magnetic builds, falls, and builds again in the other direction according to the direction of the current. That is what Maxwell's equations are telling us. The equation is Voltage (V) = L * (di/dt) An inductor that accumulates the magnetic field is also called a choke because it builds and collapses to oppose the current. As the current increases, the magnetic field builds (pulls energy out of the current) to oppose the current, as the current increases; and the magnetic field collapses and injects energy back into the circuit as the charges. Now to field theory. If you put a positive voltage at the end of one wire and a negative charge at the other end of the wire, you are actually establishing an electric field in the wire conductor. If the charges do not vary in time (DC), you get a "static electric field". If the charges vary in time (AC) you get a "dynamic electric field." Along with the electric field, a magnetic field is developed at a 90 degree angle to the electric field. So, an electric field established along a conductor runs parallel to the conductor, establishes a magnetic field that is perpendicular to the conductor. There is a convention called the right hand rule. Clench a fist on your right hand, stick your thumb in the direction of positive current flow and the fingers will point to the direction of the magnetic field. Notice that the two fields are orthogonal to each other (that is pointing to different directions by 90 degrees) The same is true for an alternating field. The magnetic field is perpendicular to the electric field, but it is out of phase with the electric field by a quarter wave. The two fields are not independent of each other because one induces the other and the other induces the one. This is how electro-magnetic fields propagate through space. The electric field generates a magnetic field that generates another electric field that generates another magnetic field and on and on and on and on out into space until your radiation dissipates to an undetectable level. It is like a wave of water at sea. So the parts of your questions I can answer are: 1) "does an electron emit electro-magnetic radiation when it is moving at a constant velocity, and in a straight line?" An electron loses potential energy but gains kinetic energy as it moves down an electric field. In the DC case, an electron moving down a conductor in a straight line (linear electric field) at a constant velocity generates a constant (magnitude and direction) magnetic field. 2) "Both of these fields are changing but not like in the case of particle acceleration." The E-M fields change dynamically only in the AC case. DC case (static) EM fields are of constant magnitude and direction. A sine wave function can be considered the path of a particle that is subjected to a constant acceleration in the opposite (negative) direction of the particle's travel. In the AC case the EM fields build and collapse as the current travels in one direction, decelerates, and starts moving in the other direction. 3) "So, does an electron emit electro-magnetic radiation when it is moving at a constant velocity, and in a straight line?" An electron moving down a constant (DC) electric field generates a constant magnetic field with it. A moving magnetic field will induce charge movement in an electric field. I looked at Larmour's equation at: http://www.cv.nrao.edu/course/astr534/LarmorRad.html It discusses E-M radiation of an "accelerating" charge. Seems to be analogous to the AC situation I am talking about because a sine wave can be defined as the path of a particle that experiences a constant acceleration force in the negative direction it is traveling. So if a charge is "accelerating" in one direction, the choke action of the magnetic field will subtract energy from the system by building a magnetic field, and will collapse the magnetic field when the charge is negatively accelerating. 4) "Both of these fields are changing but not like in the case of particle acceleration." The elctro-magnetic (EM) field only changes in the AC case. If a sine wave is the function of a negative acceleration, this is the accelerating case. 5) "The two fields appear to be independent of each other caused by different mechanisms." The two fields are NOT independent of each other. One induces the other and the other induces the other. Sincere regards, Mike Stewart Click here to return to the Physics Archives

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