Coulombs Law Electric Field from Multiple Charges Integration
![Coulomb’s Law • Electric Field from Multiple Charges • Integration of Volume charge • Coulomb’s Law • Electric Field from Multiple Charges • Integration of Volume charge •](https://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-1.jpg)
Coulomb’s Law • Electric Field from Multiple Charges • Integration of Volume charge • Electric Field near Infinite Wire • Electric Field near Infinite Sheet • Electric Field between two Infinite Sheets • Field Lines • Streamlines
![Coulomb’s Law • Coulomb’s Law •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-2.jpg)
Coulomb’s Law •
![Example of Coulomb’s Law • Example of Coulomb’s Law •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-3.jpg)
Example of Coulomb’s Law •
![Electric Field • Electric Field •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-4.jpg)
Electric Field •
![Electric Field from Multiple Charges • Electric Field from Multiple Charges •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-5.jpg)
Electric Field from Multiple Charges •
![Example – Electric Field from 4 charges • Example – Electric Field from 4 charges •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-6.jpg)
Example – Electric Field from 4 charges •
![Continuous Charge - Integration of Charge • Continuous Charge - Integration of Charge •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-7.jpg)
Continuous Charge - Integration of Charge •
![Integration of Charge (cont) • Integration of Charge (cont) •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-8.jpg)
Integration of Charge (cont) •
![Continuous Charge - Other examples • Continuous Charge - Other examples •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-9.jpg)
Continuous Charge - Other examples •
![Continuous Charge -Middle Example • Continuous Charge -Middle Example •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-10.jpg)
Continuous Charge -Middle Example •
![Continuous Charge -Field near infinite line charge • Continuous Charge -Field near infinite line charge •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-11.jpg)
Continuous Charge -Field near infinite line charge •
![Field near infinite line of charge (cont) • Field near infinite line of charge (cont) •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-12.jpg)
Field near infinite line of charge (cont) •
![Field near infinite sheet of charge • Field near infinite sheet of charge •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-13.jpg)
Field near infinite sheet of charge •
![Field near infinite sheet (cont) • Field near infinite sheet (cont) •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-14.jpg)
Field near infinite sheet (cont) •
![Electric Field between 2 Infinite Sheets • Electric Field between 2 Infinite Sheets •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-15.jpg)
Electric Field between 2 Infinite Sheets •
![Field Lines • Field lines – Point in direction of electric field – Direction Field Lines • Field lines – Point in direction of electric field – Direction](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-16.jpg)
Field Lines • Field lines – Point in direction of electric field – Direction + test charge moves – Originates on +Q terminates on -Q – Cross-sectional density proportional to E magnitude
![Streamlines • Streamlines •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-17.jpg)
Streamlines •
![Streamlines • Streamlines •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-18.jpg)
Streamlines •
![Streamline Example • Streamline Example •](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-19.jpg)
Streamline Example •
![Example problem 1 1. 3 point charges are in xy plane; with 5 n. Example problem 1 1. 3 point charges are in xy plane; with 5 n.](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-20.jpg)
Example problem 1 1. 3 point charges are in xy plane; with 5 n. C at y= 5 cm, -10 n. C at y =-5 cm, and 15 n. C at x=-5 cm. Find position of 20 n. C that exactly cancels field at origin. - Add first 3 fields to get resultant as function of ax , ay (like example 2. 2) - 4 th charge must exactly cancel field with same combination of ax , ay - Write in general field form as magnitude times unit vector - Equate magnitudes
![Example problem 2 7. A 2 u. C charge is located at A(4, 3, Example problem 2 7. A 2 u. C charge is located at A(4, 3,](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-21.jpg)
Example problem 2 7. A 2 u. C charge is located at A(4, 3, 5) in free space. Find Eρ, Eφ, and Ez at P(8, 12, 2) - Get field in rectangular coordinates as function of ax, ay, az - translate rectangular variables to cylindrical variables - translate rectangular unit vectors to cylindrical variables.
![Example problem 3 13. A uniform charge density extends throughout a spherical shell from Example problem 3 13. A uniform charge density extends throughout a spherical shell from](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-22.jpg)
Example problem 3 13. A uniform charge density extends throughout a spherical shell from r=3 cm to r=5 cm. Find the total charge and the radius containing half the charge.
![Example problem 4 • Find the electric field on the z-axis produced byan annular Example problem 4 • Find the electric field on the z-axis produced byan annular](http://slidetodoc.com/presentation_image_h/7637619fa7f7b52a45588633a6c964a2/image-23.jpg)
Example problem 4 • Find the electric field on the z-axis produced byan annular ring z= 0, a <ρ <b, 0 < φ < 2π
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