Calculation of potential of an grounded sphere ball with charges

[henry407]

Homework Statement

Consider an originally neutral conductor sphere of radius R with a cavity and a point charge Q1 inside the cavity.
(a)The conductor is grounded. Find the electric potential outside the conductor and the total charge on the conductor.

Homework Equations

The Attempt at a Solution

As shown on the figure I draw, I conclude that the E-field and the potential is zero by gauss law. Somehow, I think that is not possible as this question is followed up by 3 other questions which related to its potential. I hope someone could point out the mistake of the figure. Thanks a lot~

 

[henry407]

Help~