Physics 201- Introduction to Electricity & Magnetism
September 6- Visualizing & Calculating Electric Fields

Multiple Charges & 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.

 Common notation for charge density SI Units of charge density "Small volume chunk" (with Cartesian version) "Small chunk of charge" Point charge q C Line charge distribution (1-D) l C/ m dl = dx dq = l dl Surface charge distribution (2-D) s C/ m2 dA = dx dy dq = s dA Volume charge distribution (3-D) r C/ m3 dv = dx dy dz dq = r dv

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 Jeff Phillips phillips@lmu.edu Loyola Marymount University Fall 2002