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I understood that the electric field inside a conductor placed in the external electric field is zero

But in a cavity made of a conductor the electric field is zero is quite contradicting .

Let us suppose a cavity is placed in the external electric field Its face coming in contact with the incoming field lines acquire positive charge and the *opposite side of that face acquire an equal negative charge * and the same thing happens on the opposite face of the cavity We will see that inside a cavity two faces with opposite charge density will form so same electric field must be present inside and outside the cavity

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When speaking about cavity, it means that its faces are connected by a conductor. Thus, if there are electric field lines going from one face to the other, then these two faces have different potentials, and the electrons will flow to the region with higher potential - until the potentials equilibrate.

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