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Faraday's law in the integral form can be stated as $V = -d\Phi/dt$, where the right-hand side represents the rate of change of the magnetic flux and the left the voltage difference. In other words, a changing magnetic flux generates a voltage.

My question is if a constant voltage would generate a changing magnetic flux.

If it does, then why is a.c. used in transformers? Even for d.c. currents to flow, a voltage must be present, so if there was a d.c. current in the primary, then there would be a voltage, and so, by Faraday's law, a changing magnetic flux. Also, if a.c is required, then what equation says that only a changing current generates a magnetic field?

Finally, does Ampère's law work both ways? That is, does a circulating magnetic field produce a current flow?

Thanks for the answers.

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  • $\begingroup$ Can you specify your logic behind your opinion "a constant voltage would generate a changing magnetic flux."? $\endgroup$ – SchrodingersCat Oct 23 '15 at 7:47
  • $\begingroup$ By Faraday's law, V = -dø/dt, so if there is voltage, there is a rate of change of flux. Since the left hand side of the equation is not a rate of change, but the actual value of the voltage, it does not matter whether the voltage is changing or not; it would still generate a changing magnetic flux. $\endgroup$ – Halif Khazhaman Oct 23 '15 at 7:51
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    $\begingroup$ Leave the formula, do you know the actual LAW from where the formula has been derived? I mean the fact that magnetic flux is changing, so to conserve energy, an emf is $\mathbb{INDUCED}$? The law does not say things like " if there is voltage, there is a rate of change of flux" and vice versa. $\endgroup$ – SchrodingersCat Oct 23 '15 at 7:59
  • $\begingroup$ So Faraday's law does not work both ways then? And Ampere's law neither? By "so as to conserve energy", do you mean Lenz law? $\endgroup$ – Halif Khazhaman Oct 23 '15 at 8:11
  • $\begingroup$ Yes. The three laws together give the complete meaning. Do not judge what a law means or tries to say simply from the formula or results borne from it. Check what the statement of the law has to say. $\endgroup$ – SchrodingersCat Oct 23 '15 at 8:18
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The fact of the matter is that a DC current induces a constant magnetic field, except for the instant at which it commences and ceases. If a square wave, for example, were applied to the primary of a transformer, the secondary would produce a series of spikes of alternating polarity (as in an automotive ignition coil). Voltage can be transformed by a DC-to-DC converter, which works by generating an AC current, applying it to a transformer, and rectifying the output of the secondary, but the cost is higher than when using a transformer. (This is an oversimplification, but the details are not the question here.) Transformers and induction motors require an AC current. Take the case of a high voltage (up to 1,000,000 volts) long distance transmission line. It operates at the high voltage to reduce losses, but the voltage is obviously unsuitable for either generation or local distribution, thus requiring transformers to change the voltage. It is much more economically feasible to use an AC system from one end to the other. (Nowadays, since the advent of cost effective and reliable high-power semiconductors, some high voltage transmission lines are operated at DC, requiring conversion at both ends.) So, the answer to your question about why AC is used: it's cheaper.

For an interesting take on the matter, look up the battle between Edison Electric Light, which advocated DC distribution and Westinghouse Electric Company, which chose AC.

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The key thing about transformers is their primary winding's magnetic field only induces currents in the secondary winding(s) during that time while that field is in motion, same as an alternator or generator.

The field can be put in motion by machinery as in the alternator or generator, or the field can be put in motion (as in the stationary transformer primary winding) by varying the primary winding input voltage, causing the field to move or pulsate (rise\fall,expand\collapse, etc), whilst the winding is stationary.

Of course if the transformer primary winding requires constant input voltage change, using an AC voltage source is a natural fit. If you had a DC source, you'd have to build something to turn it into AC (or at least pulses of dc) before sending it into the transformer.

I have never seen a coil with a constant current produce changing flux, unless that coil (or another in the vacinity) was mounted on moving machinery.

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