The potential at the center of the sphere

[chan1]

Homework Statement

the electric field at the surface of a charged, solid, copper sphere with radius 0.160m is 3600N/C , directed toward the center of the sphere.
what is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?
answer in V
thanks



. The attempt at a solution
v=u/q
how to find the u and q thanks

 

[vanhees71]

Think about what's the electric field inside the sphere (copper is a conductor!).

 

[chan1]

Think about what's the electric field inside the sphere (copper is a conductor!).

Q=R^2E/k , v=kQ/R
use these two?

 

[STEMucator]

Pretty sure there was a theorem that said the electric field inside an isolated conductor is zero, but the potential has the same value at all points on the surface whether inside the surface or not. That is, the potential is the same at the center as it would be anywhere else on the conductor.

This is because the charge distributes itself uniformly on the surface of a spherical conductor.

 

[paranormal]

I would like to clarify that the potential at the center of a sphere is not dependent on the charge or the material of the sphere. It is solely determined by the distance from the center of the sphere to a reference point, usually taken to be infinitely far away.

In this case, the potential at the center of the sphere can be calculated using the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge on the sphere, and r is the distance from the center. Since the potential is zero at infinity, we can set r = ∞ and calculate the potential at the center of the sphere as V = kQ/∞ = 0V.

However, if we want to find the potential at a specific distance from the center, we need to know the charge on the sphere and the distance from the center. In this case, the charge on the sphere can be calculated using the electric field at the surface, as E = kQ/r^2. Therefore, Q = Er^2/k. Once we have the charge, we can use the formula V = kQ/r to calculate the potential at the desired distance from the center.

In summary, the potential at the center of a sphere is zero if we take the potential to be zero at infinity. To find the potential at a specific distance from the center, we need to know the charge on the sphere and the distance from the center.