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A current carrying wire has a magnetic field around it but no electric field.There will be electric field around a body only if it has static electricity.In this wire, charges(electrons) are moving.The number of charges entering is equal to number of charges leaving the conductor.So it remains neutral.A neutral body cannot have an electric field around it.

ACTUALLY, there IS also an electric field. A current is made up of moving charges, and all charges (moving or static) create an electric field.

Materials that have a neutral charge are not good conductors and therefore would not have a current going through them in the first place.

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