To solve this problem, we will use the formula for the electric field due to a point charge,$\\ E = \frac{kQ}{r^2},$ where $k = \frac{1}{4\pi\varepsilon_0}$ and $Q$ is the charge.$\\$Given:$\\$• Radius of the spherical conductor $= 10$ cm$\\$• Charge $Q = 3.2 \times 10^{-7}$ C$\\$• Distance from the center of the sphere $r = 15$ cm$= 0.15$ m$\\$• $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9$ N m$^2$ C$^{-2} \\$Since the point is outside the sphere, we can treat the sphere as a point charge located at its center.$\\$Substitute the known values into the formula:$\\ E = \frac{9 \times 10^9 \cdot 3.2 \times 10^{-7}}{(0.15)^2} \\$Calculate the denominator:$\\ (0.15)^2 = 0.0225 \\$Calculate the electric field:$\\ E = \frac{9 \times 10^9 \cdot 3.2 \times 10^{-7}}{0.0225} \\ E = \frac{28.8 \times 10^2}{0.0225} \\ E = 1.28 \times 10^5$ N/C$\\$Therefore, the magnitude of the electric field at a point 15 cm from the center of the sphere is $1.28 \times 10^5$ N/C$. \\$This corresponds to Option 1.