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No external fields penetrate the conductor as they are canceled at the outer surface by the induced charge.

My question is why is field inside conductor zero when there is no other field inside the conductor to cancel the field due to the induced charges?

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My question is why is field inside conductor zero when there is no other field inside the conductor to cancel the field due to the induced charges?

I believe you're misinterpreting the phrase "no external fields penetrate the conductor".

In the electrostatic case, the net electric field within a conductor is zero. But the net internal electric field is the superposition of

(1) the electric field due to charge external to the conductor

(2) the electric field due to the charge distribution on the surface of the conductor

So, in a sense, the external electric field is inside the conductor but there is also there an electric field (from induced charge distribution on the surface) that, together, add up to zero.

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At every point in space (both inside and outside of the conductor), the electric field is the vector sum of the externally applied field and the induced field created by the rearrangement of charges on the surface of the conductor.

The induced charges produce a field which is equal and opposite to the applied field inside the body of the conductor, so the total electric field vanishes.

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