Many people just think they know the answers!
Inductive components like motor winding resist sudden changes in current. That's because the magnetic field caused by the current needs time to build up or decrease. That means that when current is flowing and this is suddenly cut off, the winding will try to maintain that current, and becomes a power source generating a voltage to be able to do so. It gets its power from the built up magnetic field.
Since the winding is now a power source instead of a consumer the voltage is reversed for the same current flow direction. That also explains how the voltage on a coil can become higher than the power supply: instead of subtracting the voltage over it you add it to the power supply. That's why you need a flyback diode on for instance a relay coil: the diode will allow the back emf to flow back to the power supply without damaging the switching transistor.
When a current flows through a conductor it generates a magnetic field around the conductor. with that being said in a solenoid the exact process take place, The magnetic fields around each turn on the coil link with the rest of the other fields on other turns to form complete loops around on the out side and the inner core of the coil. These line of flux will determine the polarity and strength of the solenoid. No matter how tight are the turns there will be flux lines that will always remain around each turn, these smaller flux lines will induce a current in the coil when there is an applied voltage(these currents that are induced are known as Eddy currents). But when these currents are induced they will be in a opposite direction with the applied current and since it is in a counter direction therefore it is known as the back EMF.
Counter-electromotive force
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The counter-electromotive force also known as back electromotive force (abbreviated counter EMF, or CEMF)[1] is the voltage, or electromotive force, that pushes against the current which induces it. CEMF is the voltage drop in an alternating current (AC) circuit caused by magnetic induction (see Faraday's law of induction, electromagnetic induction, Lenz's Law). For example, the voltage drop across an inductor is due to the induced magnetic field inside the coil, and is equal to the current divided by the impedance of the inductor.[1][2] The voltage's polarity is at every moment the reverse of the input voltage.[1][3]
The term Back electromotive force, or just Back-EMF, is most commonly used to refer to the voltage that occurs in electric motors where there is relative motion between the armature of the motor and the magnetic field from the motor's field magnets, or windings. From Faraday's law, the voltage is proportional to the magnetic field, length of wire in the armature, and the speed of the motor. This effect is not due to the motor's inductance and is a completely separate effect.
In a motor using a rotating armature in the presence of a magnetic flux, the conductors cut the magnetic field lines as they rotate. This produces a voltage in the coil; the motor is acting like a generator (Faraday's law of induction.) at the same time it is a motor. This voltage opposes the original applied voltage; therefore, it is called "back-electromotive force" (by Lenz's law). With a lower overall voltage across the armature, the current flowing into the motor is reduced.[4] One practical application is to use this phenomenon to indirectly measure motor speed and position since the Back-EMF is proportional to the armature rotational speed.[5]
In motor control and robotics, the term "Back-EMF" often refers most specifically to actually using the voltage generated by a spinning motor to infer the speed of the motor's rotation for use in better controlling the motor in specific ways.[6]
To observe the effect of Back-EMF of a motor, one can perform this simple exercise. With an incandescent light on, cause a large motor such as a drill press, saw, air conditional compressor, or vacuum cleaner to start. The light may dim briefly as the motor starts. When the armature is not turning (called locked rotor) there is no Back-EMF and the motor's current draw is quite high. If the motor's starting current is high enough it will pull the line voltage down enough to notice the dimming of the light
https://www.youtube.com/watch?v=VfvfkXhHw04I don't need to add any more, this says it all!
Tom