Average Charge Density in a Region : 
Charge Density at a Point :  


Three Main Types of Charge Distributions:




Charge on a Line  Charge on a Surface  Charge in a Volume  
Charge Distribution: (SI Units) 
(C/m) 
(C/m^{2}) 
(C/m^{3}) 
Differential Charge: 



Total Charge: 
Electric Field Due To A Differential Charge
The general idea is to imagine that you replace charge distribution by an infinite number of differentially small charges dq that fill the region where the charge is distributed. Then pick one dq so that it is located at some representative location in the charge distribution.
Using this dq as a source, determine the Efield at the point where you want to know its value

_{} _{} _{} 
If you could move the dq all around inside of the charge distribution and sum up all the contributions from each dq, you would obtain the value of the Efield . You accomplish this task by integrating dq over the charge distribution.
The magnitude of dq can be determined if you know (or can calculate) the type of charge density involved l, s, or r.
Replacing dq by the appropriate charge density you can turn the intergrals over charge into a spacial intergrals which can be integrated to find the components of the Efield. For a specific example see calculus derivation of the Efield near a infinite line charge