- #1
prosteve037
- 110
- 3
Homework Statement
I am having trouble understanding how
[itex]\textit{Δ}\vec{E}\textit{ = k}_{e}\frac{Δq}{{r}^{2}}[/itex]
(where ΔE is the electric field of the small piece of charge Δq)
turns into
[itex]\vec{E}\textit{ = k}_{e}\sum_{i}\frac{{Δq}_{i}}{{{r}_{i}}^{2}}[/itex]
then into
[itex]\vec{E}\textit{ = k}_{e} \lim_{Δq→0}\sum_{i}{\frac{{Δq}_{i}}{{{r}_{i}}^{2}}}[/itex]
which finally takes the form
[itex]\vec{E}\textit{ = k}_{e}\int{\frac{dq}{{r}^{2}}}[/itex]
Homework Equations
- Listed Above -
The Attempt at a Solution
I understand the summation part, which just takes the sum of all the electric fields of each individual part of the continuous charge distribution.
What I don't understand is the latter part, where the limit is taken of the summation and then turned into an integral. What's going on there and why is that done?