Charged Sphere

Definition

A charged sphere is a three-dimensional object with a uniform distribution of electric charge throughout its volume. The electric field and potential generated by a charged sphere are important concepts in the study of electrostatics.

5 Must Know Facts For Your Next Test

1. The electric field inside a charged sphere is constant and directed radially outward from the center of the sphere.
2. The electric field outside a charged sphere is the same as the field of a point charge located at the center of the sphere, and it decreases with the square of the distance from the center.
3. The electric potential inside a charged sphere varies linearly with the distance from the center, while the potential outside the sphere varies inversely with the distance from the center.
4. The total charge of a charged sphere is equal to the product of the charge density and the volume of the sphere.
5. The capacitance of a charged sphere is proportional to its radius, and it is independent of the charge distribution within the sphere.

Review Questions

• Explain the relationship between the electric field and electric potential inside a charged sphere.
  • Inside a charged sphere, the electric field is constant and directed radially outward from the center. The electric potential varies linearly with the distance from the center, such that the potential is highest at the surface of the sphere and decreases towards the center. This relationship between the electric field and potential is a consequence of the uniform charge distribution within the sphere and can be derived from the fundamental principles of electrostatics.
• Describe how the electric field and electric potential of a charged sphere differ inside and outside the sphere.
  • Inside the charged sphere, the electric field is constant and the potential varies linearly with distance from the center. Outside the sphere, the electric field decreases with the square of the distance from the center, just as the field of a point charge located at the center of the sphere. Similarly, the electric potential outside the sphere varies inversely with the distance from the center, again like a point charge. This difference in the behavior of the field and potential inside and outside the sphere is a result of the uniform charge distribution within the sphere.
• Analyze how the capacitance of a charged sphere is related to its radius and charge distribution.
  • The capacitance of a charged sphere is proportional to its radius and independent of the charge distribution within the sphere. This is because the capacitance of a conductor is determined by its geometry, not the specific arrangement of charge. For a charged sphere, the capacitance is given by the formula $C = 4 extbackslash pi extbackslash epsilon_0 R$, where $R$ is the radius of the sphere and $ extbackslash epsilon_0$ is the permittivity of free space. This relationship highlights the importance of the sphere's size in determining its ability to store electric charge, which is a fundamental property in the study of electrostatics.

Related terms

Electric Field:

The electric field is a vector field that describes the strength and direction of the electric force experienced by a charged particle at a given location in space.

Electric Potential:

The electric potential is a scalar field that describes the potential energy per unit charge of a charged particle at a given location in space.

Coulomb's Law:

Coulomb's law is the fundamental principle that describes the force between two stationary, electrically charged objects.