A21-Lect-5+%5BCompatibility+Mode%5D

A21-Lect-5+%5BCompatibility+Mode%5D - 1/24/2009 Ex: The fig...

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1/24/2009 1 Ex: The fig (a) shows a thin, uniform charged rod of length L with total charge Q that can be either positive or negative. Find the electric field strength at distance r in the plane that bisects the rod. Solve: follow the 5 steps of the solving strategy (a) • The y-components of the two fields cancel each other. We left with the x-components of the electric field at P. • We divided the rod into little segments, so we can treat them as a point charges. • We know how to find the electric field of a point charge (here the segment i ). • Thus, the x-component of E i is: + = = + = i i i i Q Q r y r r r and r y r where 2 2 i 2 2 1 1 cos θ i i i i x i r Q E E π cos 4 1 cos ) ( 2 0 = = = = + = = + = + + = N i i N i x i x i i i x i r y Q r E E et onent we g net x-comp The r y r r y r r y E Thus 1 2 / 3 2 2 0 1 2 / 3 2 2 0 2 2 2 2 0 ) ( 4 1 ) ( , ) ( 4 4 ) ( ,
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1/24/2009 2 • Now we need to use he concept of linear charge density, which gives, • We want to let then the length . Now we can replace the sum with an integral ranging from as shown in the fig , ) ( = = as, te E we can wri Thus y L Q y Q x λ = + = N i i x r y y r L Q E 1 2 / 3 2 2 0 ) ( 4 π N dy y 2 2 L y to L y = = in the fig.
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This note was uploaded on 02/21/2009 for the course PHY A10 taught by Professor Tawfiq during the Fall '08 term at University of Toronto- Toronto.

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A21-Lect-5+%5BCompatibility+Mode%5D - 1/24/2009 Ex: The fig...

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