How to Scale Gradient Field for large z-values?

I want to plot a function R^2 -> R with gradient Field beneath:

f2 = @(x,y) 1./sqrt(x.^2+y.^2);
[u2,v2] = meshgrid(-1:0.01:1);
[du2,dv2] = gradient(f2(u2,v2));
s = surf(u2,v2,f2(u2,v2));
hold on

contour(u2,v2,f2(u2,v2))
hold on

norm = 1./sqrt(du2.^2+dv2.^2);
quiver(u2,v2,du2./norm,dv2./norm,'LineWidth',2)
axis([-1 1 -1 1 0 10])

caxis([0,10])
colormap(cool)
alpha(s,0.95)
shading flat

Sadly the gradient field is not visible. Probably because it's too small, f2 get's too large and I'm lacking of the mathmatical knowledge to adjust it properly