(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

- Listed Above -

3. 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?

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# Homework Help: Formula for the Electric Field Due to Continuous Charge Distribution

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