A metallic solid sphere of radius R is given the charge Q. Which of the followingstatement is true then

To analyze the situation of a metallic solid sphere with a charge $Q$, let's break down the relevant concepts.

1. Nature of Charge on Conductors: Charges reside on the surface of a conductor. In the case of a metallic solid sphere, any excess charge $Q$ will distribute itself uniformly over the surface because of the repulsion between like charges.

2. Electric Field Inside and Outside the Sphere:

   • Inside the Sphere: The electric field inside a conducting sphere is zero. This is because any charge in motion will redistribute until equilibrium is reached, resulting in no net electric field inside the conductor.
   • Outside the Sphere: The electric field at a distance $r$ from the center of the sphere (where $r > R$) behaves as if all the charge were concentrated at a point at the center. The electric field $E$ at this distance can be calculated using the formula: $E = \frac{1}{4\pi \epsilon_0} \cdot \frac{Q}{r^2}$

3. Surface Charge Density: The surface charge density $\sigma$ on the sphere can be found using the formula: $\sigma = \frac{Q}{4\pi R^2}$

With these concepts in mind, we can conclude the following:

Final Summary

• The electric field inside the metallic solid sphere is zero.
• The charge $Q$ distributes uniformly over the surface.
• The electric field outside the sphere can be described by Coulomb's Law as if the charge were concentrated at the center.

Thus, the correct statement is that the electric field inside the sphere is zero and that the charge resides uniformly on the surface.