# Electromagnetic field emitted by a charge

1. Oct 21, 2006

### 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.

2. Oct 21, 2006

### OlderDan

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. Oct 21, 2006

### Staff: Mentor

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. Oct 28, 2006

### pmb_phy

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. Oct 28, 2006

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

6. Oct 28, 2006

### pervect

Staff Emeritus
Last edited by a moderator: Apr 22, 2017
7. Oct 30, 2006

### Meir Achuz

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: Apr 22, 2017