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Definition:. Electric Fields II. Electric fields are produced by point charges and continuous charge distributions. is force exerted on charge by an external field . Note: q produces a field but it is not external. B : (0,y). a. a. A : (x,0). x. -q. +q.

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Electric fields ii l.jpg

Definition:

Electric Fields II

Electric fields are produced by point charges

and continuous charge distributions

is force exerted on charge by an external field

Note: q produces a field but it is not external


Example electric dipole l.jpg

B : (0,y)

a

a

A : (x,0)

x

-q

+q

Example: Electric Dipole

Derive an expression for at point B.

y



Slide4 l.jpg
For fun: find E at point A, and show that it is approximately proportional to x-3, at large distances x.


Continuous charge distributions l.jpg

dq

+

+

+

+

+

+

+

+

+

dE

+

+

+

Source

Continuous Charge Distributions

E = ?

  • Cut source into small (“infinitesimal”) charges dq

  • Each produces

or


Slide6 l.jpg

  • Steps:

  • Draw a coordinate system on the diagram

  • Choose an integration variable (e.g.,x)

  • Draw an infinitesimal element dx

  • Write r and any other variables in terms of x

  • Write dq in terms of dx

  • Put limits on the integral

  • Do the integral or look it up in tables.


Example uniformly charged thin rod l.jpg

L

d

Example: Uniformly-Charged Thin Rod

(length L, total charge Q)

+

+

+

+

+

+

+

+

+

Charge/Length = “Linear Charge Density”

= constant = Q/L



In 2d problems integrate components separately to obtain the electric field l.jpg
In 2D problems, integrate components separatelyto obtain the electric field:

{

x-component of


Example uniformly charged ring l.jpg
Example: Uniformly-Charged Ring

y

R

x

(x,0)

Total charge Q, uniform charge/unit length,

radius R

Find: E at any point (x, 0)



Example uniformly charged semicircle l.jpg

y

R

x

Example: Uniformly-Charged Semicircle

+

+

+

+

Charge/unit length, , is uniform

Find: at origin



Summary l.jpg
Summary

  • Field of several point charges qi:

  • Field of continuous charge distribution: