Coulombs Law Electric Field from Multiple Charges Integration

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Coulomb’s Law • Electric Field from Multiple Charges • Integration of Volume charge •

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 •

Example of Coulomb’s Law •

Example of Coulomb’s Law •

Electric Field •

Electric Field •

Electric Field from Multiple Charges •

Electric Field from Multiple Charges •

Example – Electric Field from 4 charges •

Example – Electric Field from 4 charges •

Continuous Charge - Integration of Charge •

Continuous Charge - Integration of Charge •

Integration of Charge (cont) •

Integration of Charge (cont) •

Continuous Charge - Other examples •

Continuous Charge - Other examples •

Continuous Charge -Middle Example •

Continuous Charge -Middle Example •

Continuous Charge -Field near infinite line charge •

Continuous Charge -Field near infinite line charge •

Field near infinite line of charge (cont) •

Field near infinite line of charge (cont) •

Field near infinite sheet of charge •

Field near infinite sheet of charge •

Field near infinite sheet (cont) •

Field near infinite sheet (cont) •

Electric Field between 2 Infinite Sheets •

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 + test charge moves – Originates on +Q terminates on -Q – Cross-sectional density proportional to E magnitude

Streamlines •

Streamlines •

Streamlines •

Streamlines •

Streamline Example •

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. 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, 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 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 ring z= 0, a <ρ <b, 0 < φ < 2π