To derive the electric field of a charged spherical shell from its potential, we can use the equation E = -∇V, where E is the electric field and V is the potential. This means that the electric field is equal to the negative gradient of the potential.
The formula for the potential of a charged spherical shell is V = kQ/r, where k is the Coulomb constant, Q is the charge of the shell, and r is the distance from the center of the shell.
The electric field inside a charged spherical shell is constant at all points, regardless of the distance from the center. This is because the charge distribution on the shell is symmetrical and cancels out the electric field inside.
The electric field outside a charged spherical shell can be calculated using the same formula as for a point charge, E = kQ/r^2. However, the charge Q in this case is the total charge of the shell, not just the charge at the center.
The electric field of a charged spherical shell does not depend on the thickness of the shell. As long as the charge distribution on the shell remains the same, the electric field will remain constant at all points outside the shell.