Potential of Dipole I think I am close to completing it

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    Dipole Potential
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Homework Statement



We have 2 points charges qa and qb. Qa =2 nC and is at the origin while
Qb =-10nC and is at (x0,z0)=(4,2)m.

a. Find the real potential for an arbitrary x and z.
b. Find the monopole/dipole moments.
c. Find the potential due to these moments and compare with the correct value for points along the x axis.



Homework Equations





The Attempt at a Solution


I have attached what I have done. I think I am close, but I can't get my part 'c' to check out, so I think something is wrong. Thanks.
 

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What doesn't check out? You calculated the potential due to the moments so now you should compare it with the exact value along the x axis.
 
When I was comparing the potential due to these moments with the correct value, I couldn't get them to match. Sorry, I should have explained that better.
 
Of course the two will not match exactly. That's what multipole expansion is about. The question is by how much they will differ from the correct result.
 
Oh alright, I see that now. Thanks.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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