Charge Distribution in a Solid Sphere

In order to understand the effect of removing a spherical portion from a solid sphere with uniformly distributed charge, let's first discuss the charge distribution in a solid sphere.

Charge Distribution in a Solid Sphere
- When a solid sphere is uniformly charged, the charge is distributed evenly throughout its volume.
- Each infinitesimally small volume element inside the sphere carries the same charge density, denoted by ρ (rho).
- The charge density ρ can be defined as the total charge Q divided by the volume V of the sphere: ρ = Q/V.

Effect of Removing a Spherical Portion

When a spherical portion is removed from the solid sphere, the remaining portion of the sphere will have a non-uniform charge distribution. Let's analyze this effect in detail.

1. Charge Conservation
- Before the removal, the total charge Q of the solid sphere is uniformly distributed throughout its volume.
- After removing the spherical portion, the charge Q' remaining in the sphere should be conserved.
- Therefore, the charge density ρ' in the remaining portion will increase.

2. Non-Uniform Charge Density
- The non-uniform charge distribution in the remaining portion of the sphere can be visualized as having a higher charge density towards the center and a lower charge density towards the edges.
- This is because the removed portion had a lower charge density compared to the original solid sphere.

3. Electric Field
- The electric field generated by the remaining portion of the sphere will also be non-uniform.
- The electric field will be stronger towards the center of the sphere due to the higher charge density in that region.
- As we move towards the edges of the remaining portion, the electric field will gradually weaken.

4. Net Charge
- The net charge of the remaining portion will be less than the original charge Q of the solid sphere.
- The amount of charge removed depends on the size and charge distribution of the removed portion.

Conclusion

In conclusion, when a spherical portion is removed from a solid sphere with uniformly distributed charge, the remaining portion will have a non-uniform charge distribution and a non-uniform electric field. The charge density will be higher towards the center and lower towards the edges of the remaining portion. The net charge of the remaining portion will be less than the original charge of the solid sphere.