We know that we are only looking at a difference in the nucleus. This means that all factors associated with the electron cloud will cancel out when taking a(1)/a(2). Doing this we then get:

mu(1) I(2) / mu(2) I(1). We can then isolate mu(2) and then we have:

mu(2) = mu(1) a(2)I(2)/a(1)I(1)