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In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity, I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of the shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However, there is no obvious reason why the field should also be canceled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?

In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity, I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of the shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However, there is no obvious reason why the field should also be canceled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?

In many introductory books on electrostatics you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However there is no obvious reason why the field should also be cancelled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find a proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?

In many introductory books on electrostatics, you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example, if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity, I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of the shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However, there is no obvious reason why the field should also be canceled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?

In many introductory books on electrostatics you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However there is no obvious reason why the field should also be cancelled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find a proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?

If the field inside the shell is zero this must mean the charge is zero everywhere on the inner surface. Note that this is a stronger condition that just saying the net charge on the internal surface is zero - there must be no charge anywhere on the internal surface. So an equivalent way of asking the question is to ask why is the charge everywhere zero on the internal surface?

In many introductory books on electrostatics you can find the statement that the field inside a conducting shell is zero if there are no charges within the shell. For example if we place an uncharged conducting sphere in a uniform electric field we would get something like this:

For simplicity I have drawn a uniform external field and a spherical shell, but the internal field is zero for any external field and any shape of shell.

We know the field in the metal of the conductor is zero, so the external field must induce a charge separation in the conductor and this charge separation produces a field that cancels out the external field within the metal of the shell (shaded blue in the diagram). However there is no obvious reason why the field should also be cancelled to zero in the interior of the shell.

Although it is widely stated in introductions to electrostatics that the field is zero in the interior of the shell I cannot find a proof of this. So the question is how we prove that field inside the shell is always zero whatever the external field and shape of the shell?