Why is r2 - r1 = d cos θ in the dipole potential derivation?

[MCATPhys]

I know that the potential at any point P is the sum of the two potentials of a dipole. But we make two assumptions to get an equation:

1 - the distance from the dipole to P is very large relative to the dipole distance (d)
2 - we also make the assumption that r2 - r1 = dcosθ

r2 and r1 is the distance from the dipole charges to P - how do we get cosine?

I don't understand the second assumption. Any help will be nice

 

[nickjer]

You need to explain to us what r2 and r1 is in this context. I don't have a picture in front of me so I have no idea where those vectors are pointing to.

 

[Gokul43201]

2 - we also make the assumption that r2 - r1 = dcosθ

r2 and r1 is the distance from the dipole charges to P - how do we get cosine?

1. Draw the picture - label r1, r2 and θ.

2. See if you can't find a right triangle in there which you can use ... preferably one which has a side equal to r1-r2. Make any approximations that work in the limit that r1 >> d.

3. Use this triangle to derive the above relation.