A point charge of magnitude $$+1\mu C$$ is fixed at (0, 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the centre of the sphere is :

$$V_{\text{center}} = V_q + V_{\text{induced}}$$

For an uncharged spherical conductor, the net induced charge on the surface is zero. Due to the symmetry of the sphere, the potential at its center due to these induced surface charges is $$V_{\text{induced}} = \int \frac{k \cdot dq_{\text{induced}}}{R} = \frac{k}{R} \int dq_{\text{induced}} = 0$$

Thus, the potential at the center is solely due to the point charge:

$$V_{\text{center}} = \frac{kq}{r} = \frac{9 \times 10^9 \times 10^{-6}}{0.04}$$

$$V_{\text{center}} = \frac{9 \times 10^3}{4 \times 10^{-2}} = 2.25 \times 10^5\text{ V}$$

$$\vec{E}_{\text{net}} = \vec{E}_q + \vec{E}_{\text{induced}} = 0$$

$$\vec{E}_{\text{induced}} = -\vec{E}_q$$

$$E_q = \frac{kq}{r^2} = \frac{9 \times 10^9 \times 10^{-6}}{(0.04)^2}$$

$$E_q = \frac{9 \times 10^3}{16 \times 10^{-4}} = 0.5625 \times 10^7 = 5.625 \times 10^6\text{ V/m}$$

$$E_{\text{induced}} = -5.625 \times 10^6\text{ V/m}$$