How Do You Calculate Retarded Vector Potential for a Current-Carrying Loop?

[leonne]

Homework Statement

a wire bent into a loop it looks like [URL]http://www.pitt.edu/~medart/menuglossary/arch.htm[/URL] it carries a current increases linearly with time I=kt calc retarded vector potentaik

Homework Equations

A=$$\mu$$o/4$$\pi$$ $$\int$$(k(T-r/c))/r) dl

The Attempt at a Solution

I just don't understand one part.
so i have 4 integrals first one is for the small arch second one is the length third bigger arch and last the other length on the other side.
so i have $$\int$$dl/r r is radius and so the smaller radius is a and i just have
1/a $$\int$$dl I am not sure what the integration is to in the book, they have dl=2a x^ i am not seeing how they got 2a then the straight line dx/x same for here not sure why they integrate it from a to b they got ln b/a

Also for a similar problem but with straight line why did they add a factor of 2?
A=$$\mu$$o/4$$\pi$$ 2z^ $$\int$$(k(T-r/c))/r) dz

 

[cragar]

they get ln|b/a| because they are integrating over that straight line segment at distance x away, and the radius changes from a to b . But they did it in Cartesian so they go from -b to -a but the negatives cancel once inside the log. As for the factor of 2 in the other parts i will have to think about it . But on those 2 arcs you would be integrating over the angle correct.

 

[leonne]

to late already had my final lol thanks anyways

 

[cragar]

Ya this was a problem out of Griffiths , I had to do this problem like a month ago.

 

[leonne]

yeah it is was just reviewing for finals

 

[yungman]

I was just working on this two weeks ago in Griffiths. I was going to post but I saw your response. Even after the finals, you should still try to learn it.

 

[leonne]

lol ok so how do u find the integrations?