Electromagnetic field emitted by a charge

In summary, the precise form of the electromagnetic field generated by a single charge q at a given point P and time t1, if the movement of q is described by M(t), is usually formulated in terms of the retarded electric and magnetic potentials and complicated equations. Books such as Griffiths' "Introduction to Electrodynamics" and Jackson's "Classical Electrodynamics" provide derivations of these equations. However, Jackson's book is difficult to understand, so Griffiths may be a better option. Other sources, such as Franklin's "Classical Electromagnetism" and online resources, also offer derivations and explanations of these equations. However, the Wikipedia page on relativistic electromagnetism may be confusing and provide incorrect information
  • #1
coquelicot
299
67
Hello,

What is the precise form of the electromagnetic field generated by a single charge q at a given point P and time t1, if the movement of q is described by M(t). I have seek the precise answer to this question in many books of physic, without success. I think it must be relativistic. Please, does someone have information in this subject?

thanks,
Mike.
 
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  • #2
coquelicot said:
Hello,

What is the precise form of the electromagnetic field generated by a single charge q at a given point P and time t1, if the movement of q is described by M(t). I have seek the precise answer to this question in many books of physic, without success. I think it must be relativistic. Please, does someone have information in this subject?

thanks,
Mike.
The precise answer is relativistic. It is usually formulated in terms of the retarded electric and magnetic potentials associated with charge and current densities.

http://farside.ph.utexas.edu/teaching/jk1/lectures/node20.html
 
  • #3
coquelicot said:
I have seek the precise answer to this question in many books of physic, without success.

See Griffiths, "Introduction to Electrodynamics" (2nd edition), section 9.2.2 (pp. 421-426).

Or Jackson, "Classical Electrodynamics" (2nd edition), section 14.1 (pp. 654-658).
 
  • #4
jtbell said:
See Griffiths, "Introduction to Electrodynamics" (2nd edition), section 9.2.2 (pp. 421-426).

Or Jackson, "Classical Electrodynamics" (2nd edition), section 14.1 (pp. 654-658).
Jackson is extremely difficult to read, even by those who have an excellant grasp on math and EM. In my humble opinion its best to go with Griffith.

Best wishes

Pete
 
  • #5
Griffiths gives the correct answer in Eq. (9.107), but leaves out about two pages of derivation in getting to it. That's why he is simpler.
If you want a derivation (but, it's complicated), you can find one in Franklin, "Classical Electromagnetism", Sec. 15.4.2. The result is still difficult to use because it is in terms of the retarded time, which leads to all kinds of problems. For a particle moving with constant velocity, the fields can be given in terms of the instantaneous time by
[tex]{\bf E}= \frac{q{\bf r}}
{\gamma^2[{\bf r}^2-({\bf v\times r})^2]^{\frac{3}{2}}}[/tex],
and B=vXE.
 
  • #6
You might also try : http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_14.pdf

Replace the "14" in the above link with different numbers, you'll get more slides showing the derivation.

You might also try http://en.wikipedia.org/wiki/Relativistic_electromagnetism, though it's lacking diagrams at the moment.
 
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  • #7
pervect said:
You might also try : http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_14.pdf

Replace the "14" in the above link with different numbers, you'll get more slides showing the derivation.

You might also try http://en.wikipedia.org/wiki/Relativistic_electromagnetism, though it's lacking diagrams at the moment.
The Field pdf gives only the constant velocity field, which is the easy part.
The Wikipedia page is confusing, and gives the wrong answer for the E field of a moving charge. I would try to correct the Wikipedia page, but I don't want to abet a crime.
 
Last edited by a moderator:

Related to Electromagnetic field emitted by a charge

What is an electromagnetic field?

An electromagnetic field is a physical field that is created by electrically charged objects. It consists of electric and magnetic components that are perpendicular to each other and propagate through space at the speed of light.

How is an electromagnetic field emitted by a charge?

An electromagnetic field is emitted by a charge when the charge is in motion or when the charge's electric field changes. This movement or change in the electric field creates a disturbance that travels through space as an electromagnetic wave.

What are the properties of an electromagnetic field?

An electromagnetic field has several properties, including electric and magnetic fields that oscillate perpendicular to each other, the ability to travel through a vacuum, and the ability to interact with charged particles and other electromagnetic fields.

What are the effects of an electromagnetic field on matter?

An electromagnetic field can have various effects on matter, depending on the strength and frequency of the field. It can induce an electric current in conductive materials, cause polar molecules to align, and exert a force on charged particles.

How is an electromagnetic field measured?

An electromagnetic field can be measured using instruments such as an electromagnetic field meter. These devices can detect the strength and frequency of the field and are often used to assess potential health risks from exposure to electromagnetic fields.

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