# Does Faraday's law work both ways, and if so why don't we use d.c for a generator?

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?

• Can you specify your logic behind your opinion "a constant voltage would generate a changing magnetic flux."? – SchrodingersCat Oct 23 '15 at 7:47
• 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. – Halif Khazhaman Oct 23 '15 at 7:51
• 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. – SchrodingersCat Oct 23 '15 at 7:59
• 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? – Halif Khazhaman Oct 23 '15 at 8:11
• 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. – SchrodingersCat Oct 23 '15 at 8:18