Question
A wire carries an alternating current $\text{i}=\text{i}_0\sin\omega\text{t}.$ Is there an electric field in the vicinity of the wire?

Answer

When an alternating current passes through a conductor, the changing magnetic field create a changing electric field outside it. An electromagnetic field is radiated from the surface of the conductor. There is a time-varying electric ield outside the conductor. Hence, there is a time-varying electric field in the vicinity of the wire.

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