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Just hoping for a bit of help on a homework problem I'm doing at the moment...

Basically this is the question:

*Three point charges are placed along the y axis: a charge q at y=a, a charge -2q at the origin and a charge q at q=-a. Such an arrangement is called an electric quadrupole.*

a. Find the magnitude and direction of the electric quadrupole at points along the positive x-axis.

b. Use the binomial expansion to find an approximate expression for the electric field valid for x>>a. Contrast this behaviour to that of the electric field of a dipole.a. Find the magnitude and direction of the electric quadrupole at points along the positive x-axis.

b. Use the binomial expansion to find an approximate expression for the electric field valid for x>>a. Contrast this behaviour to that of the electric field of a dipole.

I've tried to do this loads of different ways...

I've basically used E = 1/4pi...q/r^2 (didn't know how do get a symbol for the permittivity of free space!) and then for the vector have put (xi - aj) for q at a and so on... But then when I add them up to come up with a total E I just get something that looks really messy - although it is to the power of a half and could be expanded using the binomial, it just looks wrong...

Any input on how I could try to solve the question would be greatly appreciated!

Thanks, Sam(antha)