Consider an inductor, resistor, battery and a switch connected in series. Explain why there is a voltage across an inductor when the current is initially switched on but after a while, there is no voltage across the inductor.
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Zaloum's Physics Discussion 
An inductor produces magnetic flux when a current is passed through it. By Lenz’s law, induced current resists the force that produced it, so conversely the magnetic field produced resists the current that created it. This forms a resistance across the inductor, resistance coupled with current means that there is a voltage drop across the inductor.
In a DC circuit, current is constant. After the initial warm-up whereby the change in current drops to 0, since change is 0 there is no opposing force. Resistance is now effectively 0, so by V=IR there is 0 voltage across the inductor
Michael, below I have copied your answer and made some small but significant changes…
An inductor produces magnetic A FIELD AROUND IT when a current is passed through it. By Lenz’s law, induced current OPPOSES the CHANGE IN MAGNETIC FLUX that produced it, so conversely the CHANGING magnetic field produced OPPOSES the current that created it. This forms AN OPPOSING VOLTAGE across the inductor THAT OPPOSES THE CURRENT FLOWING FROM THE BATTERY..
In THIS DC circuit, current is EVENTUALLY constant. After the initial CURRENT HAS BUILT TO THE MAXIMUM VALUE, THERE IS NO FURTHER change SO no opposing VOLTAGE INDUCED VOLTAGE ACROSS THE INDUCTOR.