1. Does an electric field exist within a charged spherical conductor at points other than its center?
2. Why is there no electric field at the center of a charged spherical conductor?
it does not exist.
To answer both of these questions, let's first understand the concept of a charged spherical conductor.
1. Does an electric field exist within a charged spherical conductor at points other than its center?
To determine if an electric field exists within a charged spherical conductor at points other than its center, we need to consider the properties of a conductor. In a conductor, electric charges can move freely. When a charged conductor is in electrostatic equilibrium (meaning there is no net movement of charges), the electric field within the conductor is zero. This is because the charges distribute themselves in such a way that cancels out any internal electric fields. Thus, no electric field exists within a charged spherical conductor at any point inside its surface, including points other than its center.
2. Why is there no electric field at the center of a charged spherical conductor?
The absence of an electric field at the center of a charged spherical conductor can be explained using the concept of symmetry. Suppose we have a positively charged spherical conductor. At any point on the surface of the conductor, the electric field due to the positive charges will point radially outward. By symmetry, we can conclude that the electric field at any point outside the conductor will also point radially outward.
Now, let's consider the center of the conductor. If there were an electric field at the center, it would have to point in some direction. However, any direction we choose would break the symmetry. For example, if the field pointed towards the top, it would favor the upper half of the conductor, creating an imbalance of charges. This imbalance would lead to the redistribution of charges until a new equilibrium is reached, where the electric field at the center is once again zero.
In summary, the absence of an electric field at the center of a charged spherical conductor is a result of the symmetry of the charge distribution and the redistribution of charges within the conductor to cancel any internal electric fields.