Induction by alternating voltage?

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Induction typically involves inducing a current in a conductor through a changing magnetic field from an alternating current in a coil. The discussion raises the question of whether simply alternating the voltage in a coil could also induce current in another conductor, as a changing electric field leads to a changing magnetic field. It is noted that electromagnetic waves do not require an actual current, suggesting a different perspective on induction. The relationship between alternating current and voltage is emphasized, highlighting their interdependence through inductive reactance. The conversation concludes by affirming that voltage and current in AC systems are mutually co-existing phenomena.
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The classic description of induction involves inducing a current in another conductor caused by the changing magnetic field caused by alternating current passing through a coil of wire around a metal core.

Nonetheless, wouldn't simply alternating the voltage in a coil cause induction in another conductor? My reasoning is based on a changing electric field causing a changing magnetic field. Isn't that the way an electromagnetic wave is produced? There is no actual current in an electromagnetic wave.

If I am wrong, what am I missing?
 
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If a coil has alternating current it also has alternating voltage, and vice-versa. With ac and a coil, voltage and current cannot exist independently. Inductive reactance, X is given by 2*pi*f*L. By Ohm's Law, V = I*X, I = V/X, X = V/I. They mutually co-exist.

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