Electromagnetic field emitted by a charge

[coquelicot]

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.

 

[OlderDan]

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

 

[jtbell]

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).

 

[pmb_phy]

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

 

[Meir Achuz]

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
$${\bf E}= \frac{q{\bf r}}<br /> {\gamma^2[{\bf r}^2-({\bf v\times r})^2]^{\frac{3}{2}}}$$,
and B=vXE.

 

[pervect]

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.

 

[Meir Achuz]

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.