Answer :
To determine the magnitude and direction of the electric field at a distance of 21.4 cm from the center of the spherical shell, we can consider the superposition principle.
Since the total charge on the spherical shell is uniformly distributed, it can be treated as a point charge concentrated at its center. The electric field due to the shell at the point outside of it is zero by Gauss's Law since the electric field inside a conducting shell is zero.
Therefore, we only need to consider the electric field due to the point charge at the center. The magnitude of the electric field E at a distance r from a point charge q is given by Coulomb's law: E = k * (|q| / r^2), where k is the Coulomb's constant.
Substituting the given values, we have:
E = (9 × 10^9 N·m^2/C^2) * (4.13 × 10^-6 C / (0.214 m)^2) ≈ 8,837 N/C.
The direction of the electric field is always radially outward from a positive charge. Thus, in this case, the direction of the electric field at a distance of 21.4 cm from the center of the spherical shell is outward.
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