# When -EMF is induced can we keep current the same?

I'm confused at how Back EMF or (-V, -EMF) reduces current, and conserving the overall power. Let use the following simple example to help my understanding:

A solenoid produces a magnetic field B, it consumes 300W to produce it. With 100Amps flowing at 3Volts, it has 100 Turns. A magnet with B = 0.5Tesla moves around very quickly at 0.100 Seconds, now the area of the solenoid is = 0.15 m^2 so we can use Faraday's law to predict the EMF induced within the solenoid, EMF = -N (BA)/t, thus EMF = -75V, what will happen to the input voltage and current and power?

Even if there is change in B, can we still stabilize the power at 300W? Or keep the current the same? In order to keep I stable at 100 A, what must be done?

If it is possible.

• Back-EMF reduces current when you attempt to increase current. Imagine a single coil that you immediately apply a 10V power supply across. As current begins to flow through the coil, the magnetic field being built up by the current creates an EMF that opposes the applied voltage. This literally reduces the voltage across the coil until the current has stabilized, and the back EMF disappears. The input voltage of your supply does not change at all, however the back EMF opposes your power supply, reducing its effective voltage across the coil. Thus the current and power are decreased. – krb686 Mar 23 '14 at 4:05
• However, if current was 10A before -V is induced, can 10 Amps still be sustained with the presence of -V? – Pupil Mar 23 '14 at 21:25

Let me reduce the complexity of your question by asking you to forget about power - the power you talk about is irrlevent to the question - 3 volts at 100 amps doesn't tell you anything about the magnetics - it just defines the resistance of the coil at 0.03 ohms.

Next is the permanent magnet producing a flux density of 0.5 teslas. You are questioning what voltage will be induced in the solenoid by this magnet and you are quite rightly equating B (flux density), solenoid area and time in order to calculate the induced voltage.

Well, it's a bit more complex because the flux density from a permanent magnet will not be constant and the induced voltage in the solenoid will depend on the distribution of flux from the magnet. The solenoid's area you say is 0.15 sq m or a diameter of about 0.44 metres and it is very unlikely that a magnet that can be moved around this solenoid will be producing a reasonably constant B across the whole area of the solenoid but, putting that to one side let's assume it is.

The voltage induced in a 100 turn solenoid will be 75 volts.

Keeping the current at 100A in the solenoid can still be achieved using a fairly straightforward (but powerful) current source and as the magnet moves around the solenoid you will see the terminal voltage of the current source produce 75V too. The trouble is that a real current source will not like being reversed biased because the induced voltage is alternating each time the magnet moves around the solenoid.

In fact the current flowing through the coil is irrelevant - if no dc current flowed through the coil and the magnet was moved around you'd still see an induced voltage of 75 volts.

A practical idea for a circuit that keeps the current constant is to use filtering components that block the alternating 75V at the current source but, the low speed and high current requirement make this practically impossible to achieve.

Maybe you'd like to explain your idea a little more.

• Could you explain more on how is it possible to sustain the same value of current and voltage from a powerful source with the presence of -V? And could we relate power? -- I don't really a specific idea in mind, this is just a question that allows me to understand -V's effect in a circuit etc... What detail's might you need? – Pupil Mar 23 '14 at 21:19
• Think about the solenoid being open circuit - no current flows. The induced emf from the magnet is still 75volts. A steady dc current from -100A to (and including zero) +100 A isn't affected by the induction. Power is nothing to do with it - it is incidental and only related to the $I^2$R drop. The big question is... what are you trying to do? – Andy aka Mar 23 '14 at 21:31
• I'm just experimenting to see if I can move a magnet to change the total magnetic flux and still manage to keep the solenoid's current, or any conductor for that matter constant. I wanted to know if that was even possible... From your explanations it seems so...? – Pupil Mar 24 '14 at 7:19
• I believe it can – Andy aka Mar 24 '14 at 8:15
• Could you explain a bit more as to why you believe so? So I can start studying and understanding how this can be. – Pupil Mar 26 '14 at 1:59