So, what does this mean for the physical interpretation of a point dipole?

[ShayanJ]

Mathematically,its easy to say that when the distance between the points tends to zero,for the dipole moment to stay finite,the charge should tend to infinity.
My question is,how should I interpret it?
What is a point dipole physically?
Could you give examples?
thanks

 

[mfb]

You can interpret it as a dipole which is so small that its size does not matter. This implies that all relevant distances in your problem are much larger than the size of the dipole, and higher moments (quadrupole, ...) do not matter.

 

[ashishsinghal]

...for the dipole moment to stay finite,the charge should tend to infinity.

When we say a point dipole we mean that the distance at which are calculating electric field is much greater than the distance between the charges .

eg 1cm is very small before 10km

But it does not mean that the distance itself is infinitely small. Hence charge would also be finite.