Cant understand this double integral

[transgalactic]

http://www.freeimagehosting.net/image.php?6417d9b089.gif

i don't know what it means?
what it actually does ?

how to explain its function
in words
??

 

[diazona]

1) Do you understand the meaning of the sum a couple of lines above it?
$$k\sum_i \Delta q_i \sum_j \Delta q_j \frac{(\vec{r}_j - \vec{r}_i)}{(\vec{r}_j - \vec{r}_i)^3}$$

2) Do you understand why the sum is equivalent to the integral, when the number of charges is very very large?
$$k\int_0^L \lambda \mathrm{d}l_1 \int_{2L}^{3L} \lambda \mathrm{d}l_2 \frac{1}{(l_2 - l_1)^3}$$

 

[transgalactic]

the sum is like Coulomb law but what is the meaning
of sum from i and sum from j
??

i don't know why the this sum equals this integral
??
i know that integral is a sum too
bu thy look different
there is no i and j in the integral
no L in the sum
?

 

[transgalactic]

?