Solving N-dipole Problem in the Heart: How to Calculate Potential Fields

[Carl140]

I have been trying to solve this problem without any success. Not homework, just curious how to solve this, I'm trying to deduce physical models. Honestly I have no idea
how to attack it, so I'd really appreciate if you could please provide some help.

This is electrodynamics applied to medical physics.

Suppose n-dipoles are colocated in the ventricular tissue of the heart with a certain
fixed horizontal depth, which we denote by x.
Assume all these n-dipoles have constant dipolar moment, i.e they are continuously distributed. Now imagine a system of coordinates and suppose the n-dipoles are located at the points (x,y) where x is the fixed horizontal depth and y is the height (vertical distance between the dipoles), y is varying.

How would you write the expression that describes the potential field generated by these n- dipoles? under the assumptions previously mentioned.

I know it's an integral, but don't know how to attack this problem.

Thanks in advance.

 

[quantoshake11]

at large distances you can just sum up all the dipole moments and treat it as one big dipole, i think.. Maybe you could just calculate the potential of each dipole and then sum up all the individual solutions, choosing an appropiate coordinate system (you could let a computer do this for you).