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n387g
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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
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.
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.