# lecture3 - Ele ctric Fie II lds Ele ctric fie areproduce by...

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Electric Fields II Electric fields are produced by point charges and continuous charge distributions Definition: F qE = ur r . E r q F r is force exerted on charge by an external field Note: q produces a field but it is not external

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Example: Electric Dipole Example: Electric Dipole Derive an expression for at point B. E r y a a x B : (0,y) A : (x,0) -q +q
Dipole solution:

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For fun: find E at point A, and show that it is approximately proportional to x - 3 , at large distances x .
E = ? + + + + + + + + + + + Source + Continuous Charge Distributions Continuous Charge Distributions Cut source into small (“infinitesimal”) charges dq Each produces 2 ( ) ˆ e dq dE k r = r uur dE r r dq 2 e dq dE k r = or

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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 dq in terms of dx Put limits on the integral Do the integral or look it up in tables.
Example Example : Uniformly-Charged Thin Rod : Uniformly-Charged Thin Rod

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lecture3 - Ele ctric Fie II lds Ele ctric fie areproduce by...

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