What is the initial kinetic energy of a point charge traveling at velocity v?

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In summary, when a point charge accelerates, it radiates energy due to the acceleration field. This power is shown by Larmor's formula, P=uoq^2a^2/6(pi)c. The initial kinetic energy of a point charge traveling at velocity v can be calculated using E= 1/2qv^2. However, when approaching the speed of light, the kinetic energy is the difference between the total energy and the rest energy, which is mc2 and m0c2 respectively. To accurately discuss the kinetic energy of an electron, it is more appropriate to consider charge and velocity, as charge is what causes the electric force.
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Ed Quanta
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I understand that when a point charge accelerates that it radiates energy due to the acceleration field. Larmor's formula shows the power which is radiated, and is written: P=uoq^2a^2/6(pi)c. My question is this. How can you calculate the initial kinetic energy of a point charge which is traveling at a velocity v? I understand that if the point charge is decelerating until it reaches v=0 then its kinetic energy will be less because it radiated energy away while accelerating. But I am just not sure how to numerically represent the total kinetic energy of the particle prior to decelerating. Is it just E= 1/2qv^2?
 
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  • #2
Kinetic energy for particles going at ordinary speeds is m0v2/2.

However, when getting close to the speed of light, the kinetic energy is the difference between the total energy and the rest energy. The total energy is mc2 while the rest energy is m0c2. m=m0/sqrt(1-(v/c)2).
 
  • #3
Isn't 1/2mv^2=gravitational kinetic energy? If talking about the kinetic energy of an electron, wouldn't it be more accurate to talk of kinetic energy in terms of charge and velocity since charge is what causes the electric force?
 

1. What is Larmor's formula?

Larmor's formula is a mathematical equation that describes the amount of radiation emitted by a charged particle as it accelerates. It was first developed by physicist Joseph Larmor in the late 19th century.

2. What is the significance of Larmor's formula?

Larmor's formula is significant because it helps us understand the behavior of charged particles, such as electrons, in electromagnetic fields. It is also used in various fields of science, such as astrophysics, to study the radiation emitted by celestial objects.

3. How is Larmor's formula derived?

Larmor's formula is derived using classical electromagnetic theory, specifically the laws of electrodynamics and the principles of special relativity. It is based on the concept that a charged particle undergoing acceleration will emit electromagnetic radiation.

4. What factors affect the amount of radiation emitted according to Larmor's formula?

The amount of radiation emitted according to Larmor's formula is affected by several factors, including the charge and mass of the particle, the strength of the electromagnetic field, and the acceleration of the particle.

5. How is Larmor's formula used in modern science?

Larmor's formula is used in a variety of modern scientific fields, such as particle physics, astrophysics, and medical imaging. It is also used in the design of electronic devices, such as antennas and particle accelerators.

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