Finding the electric field of a electric quadrupole

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  • #1
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One type of electric quadrupole consists of two dipoles places end to end with their negative charges (say) overlapping; that is, in the center is -2Q flanked (on a line) by a +Q to either side. Determine to electric field, E, at points along the perpendicular bisector and show that E decreases as 1/r4. Measure r from the -2Q charge and assume r>>l.


E+=E-=(1/4[tex]\pi[/tex][tex]\epsilon[/tex]0)*(Q/(r2+(l2/4)
p=Ql



The Attempt at a Solution


First I broke the electric fields into the x and y axes.
Where, Ex=0
For the Ey, I used the equation E=(1/4[tex]\pi[/tex][tex]\epsilon[/tex]0)*(p/r3)
Then, substituted p for (Q*l) and then r3 for r4
I assume there must be more to it than that, but I'm at a loss.
 

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  • #3
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Okay, so you have to add the electric fields at the +Q, -2Q and +Q.
So for +Q, E=k(Ql/(l2+r2)^(1/2)) (cos(theta)rx+sin(theta)ry)
And the for -2Q, E=k(2Ql/r2)(sin(theta)ry)
And for the other +Q, E=k(Ql/(l2+r2)^(1/2)) (-cos(theta)rx+sin(theta)ry)
Is this the correct way to do this?
 
  • #4
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+Q, E=k(Ql/(l2+r2)^(1/2)) (cos(theta)rx+sin(theta)ry)
Whats that l after Q
 
  • #5
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it's a lowercase L, for length
 
  • #6
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Using the equation where p=Ql
 
  • #7
SammyS
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Do you know about Taylor Series ?
 

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