Classical Physics: radiation due to accelerated charge

[Tim_Lou]

i've learnt that uniformly accelerated charge radiates, but why?

 

if it radiates, electric field function, E(x,y,z,t) and B(x,y,z,t) must vary sinusoidal and be orthogonal to each other and they must obey the Maxwell's equation.

 

what is the direction of the poynting vector? where can i find the solution to this problem? (i dont care about the paradox; i just want to understand the classical reasoning behind it) what do i need to consider to derive the solutions?

 

i googled electromagnetic one boy problem, accelerated charge radiation... but none of them give me any insights about the problem.(all they talk about is the paradox with equivalent principle !) can someone help me please?

[Erasmus00]

I'd suggest picking up a good E/M textbook. Purcell's textbook has an excellent chapter on the fields of moving sources, and an appendix on the same. Also, consider googling Lienard-Wiechart potentials, which are the potentials of individual moving charges.

-Will

[Tim_Lou]

thx for the info, i found some excellent online pdfs about lienard-wiechart potentials. it seems that the lorenz transformation is used, i guess thats what i was missing.

[Erasmus00]

thx for the info, i found some excellent online pdfs about lienard-wiechart potentials. it seems that the lorenz transformation is used, i guess thats what i was missing.

 

You can derive the potentials straight from Lorentz transforming a 4-current vector, but you can also solve Maxwell's equations directly. The first is easy, the second is quite a bit harder, but can certainly be done. See for instance Jackson's text.

-Will

[Farsight]

This "moving charge applet" seemed pretty good. Click on GO.

 

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

[Qfwfq]

You can derive the potentials straight from Lorentz transforming a 4-current vector, but you can also solve Maxwell's equations directly.

Of course, the two things are quite the same, once you've written the Maxwell equations in Lorentz-covariant form:

 

[math]F_{ij}u^j = j_i[/math]

 

[math]F_{ij}u_k \epsilon ^{ijkl} = 0[/math]

 

;)