That looks good, but I think the problem calls for you to use ε0 rather than k .baker265 said:Homework Statement
A spherical metal shell has charge per unit area sigma and radius R. What is the magnitude of the electric field at a distance x from the surface of the sphere? You may include only these variables in your formula: sigma, R, epsilon_0, x
Homework Equations
σ=Q/(4*pi*R^2)
k=1/(4*pi*epsilon_0)
The Attempt at a Solution
(4*pi*k*R*σ)/((R+x)^2)
The electric field inside a spherical metal shell is always zero. This is because the charges on the inner surface of the shell create an equal and opposite electric field that cancels out the electric field created by the charges on the outer surface.
The electric field outside a spherical metal shell is the same as the electric field created by a point charge located at the center of the shell. This means that the electric field is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance from the center of the shell.
If the charge on the spherical metal shell is doubled, the electric field outside the shell will also double. However, the electric field inside the shell will remain zero since the charges on the inner surface still cancel out the electric field created by the charges on the outer surface.
If a spherical metal shell is placed in an external electric field, the electric field inside the shell will still be zero. However, the charges on the outer surface of the shell will redistribute themselves in such a way that the electric field inside the shell is completely cancelled out by the external electric field.
The electric field outside a spherical metal shell is directly proportional to the size of the shell. This means that a larger shell will have a larger electric field than a smaller shell, as long as the charge on the shell remains constant. However, the electric field inside the shell will remain zero regardless of the size of the shell.