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1. In electrostatics the electric field is 0 inside a perfect conductor because otherwise there would be moving charges. The charges must redistribute themselves to make a net electric field inside the conductor 0. 2. It is possible to have an electric field inside a conductor. You can put one there by e.g. using a battery. The trick is that this prompts charges to move inside the conductor and therefore a current to develop. This is no longer electrostatics.
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