Electric Field and spherical cavities

[stunner5000pt]

Two spherical cavities of radii a and b are hollowed out from the interior of a neutral conducting sphere of radius R. At the center of each cavity is a point charge place, callthem qa and qb

a) Find the surface charges sigma a, sigma b, and sigma R.

ok say for qa

$$\vec{E} = \frac{q_{a}}{4 \pi \epsilon_{0} a^2} \hat{a} = - \vec{\nabla} V \bullet \hat{n}$$

also $$\sigma = -\epsilon_{0} \vec{\nabla} V \bullet \hat{n} = \frac{q_{a}}{4 \pi a^2}$$

but i was told this answer should be negative.. where is my mistake?

 

[OlderDan]

The total charge inside a guassian surface surrounding one inner sphere has to be zero, The surface charge must have the opposite sign of the central charge.