Step 1: Understand the concept of electric field inside a uniformly charged sphere.
For a uniformly charged sphere, whether it is a conductor or a non-conductor with uniform volume charge density, the electric field at its center is zero. This is due to symmetry. For every small charge element creating an electric field vector pointing away from the center, there is an equal and opposite charge element on the diametrically opposite side creating an electric field vector that cancels it out.
Step 2: Consider the specific case of the center (r=0).
- If the sphere is a conductor, all the charge resides on its surface. The electric field inside a conductor in electrostatic equilibrium is always zero.
- If the sphere is a non-conductor with uniform volume charge density ρ, the electric field at a distance r from the center is given by E=4πϵ01R3Qr for r≤R. At the center, r=0, so the electric field E=4πϵ01R3Q(0)=0.
In both cases, the electric field strength at the center of a uniformly charged sphere is zero.
Step 3: Compare with the given options.
The options are:
(1) 4πϵ0R2Q (This is the field at the surface)
(2) 4πϵ0RQ
(3) 4πϵ0R3Q
(4) Zero
The correct option is (4).
The final answer is (4).
3 done, 2 left today. You're making progress.