# Does the induced EMF depend on the rate if change in the total flux affecting the coil or the external flux only?

If we get a coil which is put in a changing magnetic field that increases at a constant rate, then it is known that this increase in magnetic field induces an EMF, now if the circuit is closed then this EMF creates an induced current that flows in the coil. This induced current - like any other current - creates a magnetic field around the coil. Does this magnetic filed due to the induced current interact with the external magnetic field that changes at a constant rate, hence, changing the total rate of change in magnetic flux affecting the coil and hence affecting the induced EMF value? --Or-- Does the induced EMF value depend on the rate of change of the external field and not the rate of change of total flux?

The induced EMF depends upon the rate of change of the total flux, and not just the externally applied flux.

If a current present in a wire, that current induces a magnetic field. If the current is varying the magnetic field induced by the current will vary. That varying magnetic field will in turn induce an EMF. That is the basis for the phenomenon known as self-inductance.

When a coil of wire is used as an inductor in an electric circuit, it's principle of operation is self-inductance. When a voltage is applied across the terminals of the (stand-alone) coil, current begins to flow. However, that current creates a changing magnetic field, which causes an EMF to be created which opposes the originally applied voltage. The result is that the current in the coil/inductor rises over time rather than suddenly.

So, once again, the EMF induced in a coil depends not only on an externally applied changing magnetic field, but upon the total magnetic field, including that created by the changing electric current in the coil.

• So if I get two coils and both are put in the same changing magnetic field, one is open-circuited and the other one is closed-circuited, the induced EMF in both coils are different to each other because the one with open circuit has only the rate of change of external flux while the closed circuit one has an induced current that changes the rate of flux hence induced EMF value whic again changes the induced current and the cycle continues right? Mar 19 at 15:20
• Actually, the emf induced in both coils will be affected by the current in the coil which has a closed circuit (unless the coils are oriented at right angles). The flux created by the coil with a closed circuit is strongest near the coil, but in a diminished amplitude extends through-out space. Some of that flux, possibly highly diminished, or possibly not, will extend to the open-circuit coil, and if that coil is oriented properly to encircle that flux, will cause an EMF in the open-circuit coil as well. When current in one coil causes EMF in another, that is called mutual inductance. Mar 19 at 15:32
• Yes, I meant putting them in a geometrical adjustment that would prevent any mutual induction, i.e. to see the effect of the same external changing field on the two coils! Thank you for the clear explanation. Mar 19 at 15:43

The external change in magnetic flux, causes the initial current in the wire.

This current then produces its own change in flux, which acts to slow down the currents increase ( lenz law)

The resultant total rate of change of magnetic flux is the total emf

• Thank you for the explanation! Mar 19 at 15:44