Electric Field Due to a Dipole along the dipole axis

Electric Field Due to a Dipole along the dipole axis -...

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Physics 202 Tuesday, January 26, 1999 Announcements: None Lecture notes: Example: Electric Field Due to a Dipole along the dipole axis What is the electric field E at point P due to the dipole of chares +q and -q? The electric field due to point P is the electric field due to +q added to the electric field due to -q E + = ( 1/ 4 πε o ) (q / r(+) 2 ) and E- = ( 1/ 4 πε o ) (-q / r(-) 2 ) Therefore E total = (q/ 4 πε o ) [(1/r(+) 2 ) - (1/ r(-) 2 )] If r(+) = z -(d/2) and r(-) = z + (d/2), then E total = (q/ 4 πε o ) [(1/(z - (d/2)) 2 ) - (1/ (z + (d/2)) 2 )]. Further simplification leads to E total = (q/ 4 πε o z 2 ) [(1-(d/2z)) -2 ) - (1+ (d/ 2z)) -2 )]. Usually z >>d, so we do a Taylor expansion (1-(d/2z)) -2 ) = ( 1 + 2(d/2z) + (2(3)/2!)(d/ 2z) 2 ) + .... ) and (1+ (d/2z)) -2 ) =( 1 - 2(d/2z) + (2(3)/2!)(d/ 2z) 2 ) - .... ) Therefore: E =(q/ 4 πε o z 2 ) [ 2(d/2z) + 2(d/2z)] = (q/ 4 πε o z 2 ) (2 d/z) = (qd/ 2 πε o z 3 ) We define qd =P as the dipole moment and E =(P/ 2 πε o z 3 ) P is a vector and it's direction is along the axis of the dipole, from -q
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to +q Electric Field Due to a Line of Charge Example: Problem 34, page 576 in text A conducting rod of length L
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