# Relationship between velocity and emf

### AB : Measuring RPM from Back EMF - Precision Microdrives

Generated voltage = emf = Velocity x B-field x Length. For a wire of moving with velocity v= x 10^ m/s If the angle between the velocity and magnetic field is. From the above description we can say that a relationship exists between an length of the conductor, l in meters and the rate or velocity, ν at which the magnetic field Lenz's Law states that: ” the direction of an induced emf is such that it will. The EMF induced is also proportional to the speed of the object going of induced EMF is proportional to the rate of change of magnetic flux linkage: E. M. F.

Our change in flux in this case is going to be our change in our, the magnitude of our magnetic field that is going perpendicular to the surface times the area of our surface over our change in time. What is this going to be equal to? So the change in 'B' times 'A' is really going to be 'B' times our change in area.

So what is our change in area going to be? Let's say we let delta 't'let's say delta 't' happens, what is going to be our change in area? Let's let delta 't' go on. If delta 't' goes on, this cylinder, or if we wait for 't' units of time, or if 't' units of time go by, let me do this in another color, I'm gonna use this color right over here.

## Application Notes

How far will we go after delta 't'? We know the magnitude of our velocity if you multiply the magnitude of your velocity times your change in time, that will give you your distance.

Your change in area is going to be the amount of distance it's travelled times the length of the rod, which is just that. Our change in area, which is that area right over there, our change in area over that time is going to be the distance this rod goes. Notice this rod is going in a direction that is perpendicular to the direction of the magnetic field that's an important thing to realize.

### ELECTROMAGNETIC INDUCTION

We have our change in area is going to be this dimension which is how far the rod travels times the length of the rod, that's how much area we gain, that's how much our area increases, times the length of the rod, that's our change in area. We can substitute that back over here. This is going to be equal to, we got our 'B', we have our change in time, and our change in area we just said is going to be, Let me just write it this way, I could write is as the length of our rod times the magnitude of our velocity, or our speed times our change in time.

Well, change in time divided by change in time, those cancel out. However, when the charge is traversing the moving rod it experiences an upward in the figure magnetic force of magnitude assuming that. The net work done on the charge by this force as it traverses the rod is since.

Thus, it would appear that the motional emf generated around the circuit can be accounted for in terms of the magnetic force exerted on charges traversing the moving rod. But, if we think carefully, we can see that there is something seriously wrong with the above explanation. We seem to be saying that the charge acquires the energy from the magnetic field as it moves around the circuit once in the anti-clockwise direction. But, this is impossible, because a magnetic field cannot do work on an electric charge.

Let us look at the problem from the point of view of a charge traversing the moving rod. In the frame of reference of the rod, the charge only moves very slowly, so the magnetic force on it is negligible. In fact, only an electric field can exert a significant force on a slowly moving charge.

In order to account for the motional emf generated around the circuit, we need the charge to experience an upward force of magnitude. The only way in which this is possible is if the charge sees an upward pointing electric field of magnitude In other words, although there is no electric field in the laboratory frame, there is an electric field in the frame of reference of the moving rod, and it is this field which does the necessary amount of work on charges moving around the circuit to account for the existence of the motional emf, More generally, if a conductor moves in the laboratory frame with velocity in the presence of a magnetic field then a charge inside the conductor experiences a magnetic force.

In the frame of the conductor, in which the charge is essentially stationary, the same force takes the form of an electric forcewhere is the electric field in the frame of reference of the conductor. External sensors are typically used for speed measurements, such as Hall sensors with a magnet mounted on the shaft, or transoptors with a slotted plate also mounted on the motor shaft. These sensors that can give accurate information about motor speed, required space and increase cost of parts.

In fact, the back EMF is a very important measurement for haptic feedback chips when driving vibration motors and LRAs. What is Back EMF? It is this voltage that serves as the principle of operation for a generator. The back EMF is directly related to the speed of the motor, so knowing the value of back EMF allows us to calculate the speed of that motor.

It is this voltage source that we want to measure.

When the motor is powered from constant DC voltage and not running i.