Finding Mutual Capacitance of Two Identical Metal Spherical Balls?

It is a question from the Irodov:

Find the capacitance of a system of two identical metal balls of radius $a$ if the distance between their centres is equal to $b$, with $b >> a$. The system is located in a uniform dielectric with permittivity $ε$.

My Working

I made the following assumption:

When the question says b>>a , I ignored induction between the spheres. I just found the potential difference between the capacitors .

Now Potential difference between the two surfaces should be equal to :

$Kq/a – Kq/b -(Kq/b -kq/a)$ $rightarrow $ $2(Kq/a – Kq/b)$

The next step is use to use the relation $Q=CV$ to find the capacitance .

My problem is that the solution ignored the $Kq/b$ term and just uses $Kq/a$.

It would be helpful if someone can provide an explanation for that.