For a charged conducting spherical shell of radius $R$, the electric field behavior is determined by Gauss's Law:

1. Outside the shell ($r > R$): The electric field is non-zero and given by $E = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2}$. The distance $3R/2 = 1.5R$ is greater than $R$, so this point lies outside the shell.
2. Inside the shell ($r < R$): The electric field is zero at all points inside a charged spherical shell. This is because a Gaussian surface drawn inside the shell encloses no charge ($q_{enclosed} = 0$). Furthermore, for any conductor in electrostatic equilibrium, the electric field inside is always zero , , .

Since the distance $R/2 = 0.5R$ is less than $R$, the point lies inside the shell. Therefore, the electric field is zero.