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I have a fixed wire and an electromagnet next to each other, and would like to induce continuous \$\epsilon\$ from the change of \$B\$ or \$A\$. Currently I'm focusing on changing the magnetic field, causing it to increase then decrease and so on(repeatedly) , however, not sure of the outcome of the induced \$\epsilon\$ given Faraday's law:

$$\epsilon = \frac{\phi}{\Delta t} = \frac{\Delta (BA)}{\Delta t}$$

If the magnetic field is decreasing say from \$1Tesla\$ to \$0.5Tesla\$ it's is a negative induced -\$\epsilon\$, and when its increasing from \$0.5Tesla\$ to \$1Tesla\$ that is a positive induced +\$\epsilon\$.

This seems to induce AC current? Due to the -V to +V and vice versa.

How can this be converted into DC where there is only +V?

Also, changing the area is another option and seems to give out the same results.

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What you've got is effectively a transformer, but with only one turn for your secondary winding. Transformers don't work with DC input or output, because you can't induce a DC current with a fluctuating magnetic field. To induce a DC current, the magnetic field would have to increase in magnitude without bound, which would require the current through the primary (electromagnet) to increase without bound, which is obviously impossible.

The normal approach if you need DC output is to use a rectifier and filter capacitor. A single inline diode will function as a half-wave rectifier, but that discards half of your power. Four diodes forming a full-wave bridge rectifier overcomes that problem.

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  1. Rising magnetic field causes negative EMF, dropping magnetic field causes positive EMF. Negative sign is missing in your equation. It should be something like that:

$$\epsilon = -\frac{\Delta\phi}{\Delta t} $$

  1. To induce DC current you would have to keep right side of that equation constant, which means magnetic flux rising forever to infinite. This is why DC transformers not exist.
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  • \$\begingroup\$ The sign would determine the direction of induced EMF(or induced current to be exact)? \$\endgroup\$ – Pupil Nov 19 '14 at 18:04
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    \$\begingroup\$ Yes. Lenz's law: "An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux." If change of magnetic field is positive - voltage change will be negative. \$\endgroup\$ – Kamil Nov 19 '14 at 18:18

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