# Induced emf expression in Faraday's law of induction

Magnitude of induced EMF in a loop is given as $$|\frac{d\phi}{dt}|$$. If the loop has n turns then induced EMF is given as $$|n\frac{d\phi}{dt}|$$. As we can consider each turn to be a battery which is connected in series, so net EMF is the algebraic sum of individual turn's EMF.

But the question is, as in first turn, when there is change in EMF then a current is induced to oppose the change in magnetic flux, so in subsequent turns the change in magnetic flux should be less so less EMF should be induced. Shouldn't the expression of net induced EMF in loop form a decreasing series?

• why would the emf vary from loop to loop (turn to turn) if the flux and the flux rate through every loop is the same? Jun 2, 2020 at 15:56
• If we think when a magnet is moved closer to a loop then current is induced in first turn in a way such that it oppose the change of flux and as a result overall flux rate decreases when reach to the subsequent turns.
– Manu
Jun 2, 2020 at 16:01
• I know the process occurs vey fast but shouldn't we have to take into account this effect?
– Manu
Jun 2, 2020 at 16:01
• when using the "$emf=nd\phi/dt$" formula it is assumed that the magnetic field is homogeneous; if you move a magnet even partially outside the coil this assumption is not valid. Jun 2, 2020 at 16:09

## 1 Answer

EDIT: I'd like to add that the Magnetic field travels at the speed of light. The induction of EMF might include speeds near to the speed of light. Since the magnetic field can't outrun the induction process, I am forced to think that the change in the magnetic field must be communicated to each turn simultaneously by a magnet producing a homogeneous magnetic field for $$\varepsilon=n\left|\displaystyle\frac{d\phi}{dt}\right|$$ to be true.

• Electrons move much slower than the speed of light on average. Electromagnetic waves in wires/circuits travel at speeds comparable to the speed of light, but this is not the same as the speed of electrons. What is your source for the $1/100$ figure?
– Puk
Jun 18, 2020 at 6:29
• I am sorry for that figure. I will remove it. But, isn't the drift velocity of electrons much lesser than the speed of light to cause such a sudden induction? Jun 18, 2020 at 6:37
• The drift speed of electrons is not the speed at which signals travel in a circuit, and I don't see how the former is relevant here.
– Puk
Jun 18, 2020 at 6:43
• I think I got what you're saying. Did I miss the fact that switching on lights happens almost instantaneously? Jun 18, 2020 at 6:53
• Well that would depend mostly on inductances and capacitances in the circuit, in particular the capacitance of the device. But the light starts to switch almost instantaneously. Electrons move in unison to make signals travel much faster.
– Puk
Jun 18, 2020 at 6:59