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# Electric Fields II - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about 'Electric Fields II' - cassie

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Presentation Transcript
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

a

a

A : (x,0)

x

-q

+q

Example: Electric Dipole

Derive an expression for at point B.

y

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

+

+

+

+

+

+

+

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+

dE

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+

+

Source

Continuous Charge Distributions

E = ?

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

• Each produces

or

• 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.

d

Example: Uniformly-Charged Thin Rod

(length L, total charge Q)

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+

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Charge/Length = “Linear Charge Density”

= constant = Q/L

In 2D problems, integrate components separatelyto obtain the electric field:

{

x-component of

Example: Uniformly-Charged Ring

y

R

x

(x,0)

Total charge Q, uniform charge/unit length,

Find: E at any point (x, 0)

R

x

Example: Uniformly-Charged Semicircle

+

+

+

+

Charge/unit length, , is uniform

Find: at origin

• Field of several point charges qi:

• Field of continuous charge distribution: