To solve this problem, we need to determine the electric potential and electric field at the center of a conducting sphere with radius $R$ and charge $Q. \\$For a conducting sphere, the charge is uniformly distributed on the surface.$\\$1. Electric Potential at the Center:$\\$The electric potential $V$ inside a conducting sphere is constant and equal to the potential at the surface.$\\$The potential at the surface of the sphere is given by:$\\ V = \frac{Q}{4 \pi \varepsilon_0 R} \\$Since the potential is constant throughout the sphere, the potential at the center is also:$\\ V_{center} = \frac{Q}{4 \pi \varepsilon_0 R} \\$2. Electric Field at the Center:$\\$Inside a conductor, the electric field is zero. This is because the charges redistribute themselves in such a way that the net electric field inside is zero.$\\ E_{center} = 0 \\$Thus, the electric potential and electric field at the center of the sphere are:$\\$Electric Potential: $\frac{Q}{4 \pi \varepsilon_0 R} \\$Electric Field: $0 \\$Therefore, the correct option is Option 2.