Potential Through Integration

Finite Line of Charge Pg. 724 Example 25.7

How to really do this – look in integral tables (Appendix B in your book or any calculus text)

Uniformly Charged Ring Find an expression for the electric potential at point P located on the perpendicular central axis of a uniformly charged ring of radius a and total charge Q. (Pg. 723 Example 25.5)

Integral Form 

Using V to find E In this case E is along the x axis so

Uniformly Charged Disk A uniformly charged disk has radius R and surface charge density σ. Find the electric potential at a point P along the perpendicular central axis of the disk. (Pg. 723 Example 25.6)

Using the result for a ring of charge

Using V to find E In this case E is along the x axis so