Physics 201- Introduction to Electricity & Magnetism
|September 6- Visualizing & Calculating Electric Fields|
& Continuous Charge Distributions
As you might guess from the electric field definition, fields are just like forces in that they can be added. You just have to remember that they are both vectors.
If we have a bunch of point charges we would simply
add up the field due to each point charge at the location of interest.
Consider the point charges becoming even smaller
and more numerous. Then this summation becomes an integral.
(Remember integrals are nothing more than summations of really small objects.)
Depending on how the charges are distributed, we
make have a 1-D integral (line distribution), 2-D integral (surface distribution)
or 3-D integral (solid distribution)
To get everything in terms of a common variable,
so we can integrate, we transform the small chunk of charge (dq) to look
like the charge density * a small volume chunk.
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