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The electric field inside a conductor is zero because the free electrons distribute themselves to cancel out any external electric field.
In more detail, conductors are materials that contain free electrons, which are not bound to any particular atom and can move freely throughout the material. When an external electric field is applied to a conductor, these free electrons will move in response to this field. They will continue to move until they reach a state of equilibrium, where the forces on them are balanced.
The free electrons will distribute themselves in such a way that they create an internal electric field that exactly opposes the external electric field. This is because electrons, being negatively charged, will move in the direction opposite to the external electric field. As they move, they create their own electric field in the opposite direction. Eventually, the electrons will arrange themselves so that the internal electric field they create exactly cancels out the external electric field. At this point, the net electric field inside the conductor is zero.
This is a fundamental property of conductors and is the reason why they are used in many applications, such as electrical wiring and shielding. For example, the metal casing around electrical cables acts as a shield, preventing the electric field from the cable from affecting other nearby electronics. This is because the free electrons in the metal casing rearrange themselves to cancel out the electric field from the cable, ensuring that the net electric field inside the casing (and therefore outside the cable) is zero.
It's also important to note that this only applies when the conductor is in electrostatic equilibrium, meaning that there are no net forces acting on the charges within the conductor and the charges are not moving. If the conductor is not in electrostatic equilibrium, then the electric field inside the conductor will not be zero.
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