In a meter bridge, the wire of length 1 m has a nonuniform cross-section such that, the variation$\frac{dR}{d\ell }$ of its resistance R with length $\ell$ is $\frac{dR}{d\ell }\propto \frac{1}{\sqrt{\ell }}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP ?