I need some help with these questions.
Why is there no electric field at the center of a charged spherical conductor?
Does an electric field exist within a charged spherical conductor at points other than its center?
There is no electric field inside conductors, not at the center, or anywhere else. Charges repel, and go to the surface.
It is important to note here that the reason why there is no field inside the conductor is simply due the fact that charges repel. However, the reason why the charges go to the surface is due to the inverse square Coulomb law.
Also, the fact that the electric field at the center of a spherical hollow conductor is zero only depends on the symmetry, not on Coulomb's law. But the fact that the electric field away from the center is zero does depend on Coulomb's law.
This fact has been used to test Coulomb's law, see here:
http://prola.aps.org/abstract/PRL/v26/i12/p721_1
Sure, I can help you with that!
To understand why there is no electric field at the center of a charged spherical conductor, we need to consider a few key concepts:
1. Electric Field: The electric field is a vector quantity that represents the force experienced by a positive charge in the presence of an electric field.
2. Electric Field inside a Conductor: Inside a conductor at electrostatic equilibrium, the electric field is zero. This means that there is no net movement of charges, and the charges are distributed in a way that cancels out the electric field within the conductor.
Now, let's answer your first question:
"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 symmetry.
When a conductor is in electrostatic equilibrium, any excess charge resides on its outer surface. For a spherical conductor, the excess charge resides only on the outer surface of the sphere. The inner charge distribution is equal in magnitude but opposite in sign to the outer surface charge. As a result, the electric field contributions from the inner and outer surface charges cancel each other out at the center of the conductor, resulting in no net electric field at that point.
Now, let's move on to your second question:
"Does an electric field exist within a charged spherical conductor at points other than its center?"
Within a charged spherical conductor, there is an electric field at points other than its center. However, it is important to note that this electric field exists only before the conductor reaches electrostatic equilibrium or when the conductor is not a perfect conductor. In such cases, charges redistributions may not have fully occurred.
But once the conductor reaches electrostatic equilibrium, the electric field inside the conductor becomes zero. This is because the excess charges in the conductor redistribute themselves in a way that cancels out any imbalance in electric field within the conductor.
So, to summarize:
- In a charged spherical conductor, there is no electric field at the center due to the cancellation of electric field contributions from the inner and outer surface charges.
- Before the conductor reaches electrostatic equilibrium or for imperfect conductors, there may be an electric field at points other than the center of the conductor. However, once the conductor reaches electrostatic equilibrium, the electric field within the conductor becomes zero.