When a current changes with time, it generates a changing magnetic field, according to Ampere's law. This changing magnetic field induces an electric field, according to Faraday's law of electromagnetic induction. The induced electric field produces a magnetic field that is in the opposite direction to the changing magnetic field that produced it, according to Lenz's law. This opposing magnetic field adds to the original magnetic field produced by the changing current. Is this correct?
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You are describing the radio wave that a wire with an oscillating current will produce. These fields are not induced at a single point. They are induced around thee changing fields. Consider a horizontal current producing a magnetic field around it. This changing magnetic field produces an electric field around the magnetic field change, effectively long loops of field aligned alongside the wire. These changing electric fields then produce more loops of magnetic field that end up being loops around the wire at a larger radius than the "original" magnetic field loops. The loops emanate from the current changing within the wire, traveling at the speed of light. If the current oscillates, then the fields and the resulting electromagnetic wave will oscillate at the same frequency. If the current increases at a constant rate, then the field changes would be in the changing amplitudes of the fields rather than in the oscillating directions.
