3. "Any idea how an electric brake works on a circular saw? When you let go of the trigger, the blade (or electric motor) instantly stops instead of slowing down gradually like a regular saw without an electric brake."

What a great question! I don't really know the answer - I'll try and find out - but I could have a guess. First, let me describe briefly how a motor works. A simple electric motor consists of a coil that is positioned in a magnetic field, rather like the situation shown in Figure 31.1 (although strictly speaking that figure refers to a generator). (I show a slide right at the beginning of chapter 31 that shows the arrangement also). When a current passes through the coil it produces a magnetic moment (= NIA), which we covered in Chapter 28. In turn, the magnetic field exerts a torque on the current carrying coil that tends to align the magnetic moment with the field direction. It is that torque that produces the "drive" in the motor.

Now, you notice that the coil is rotating in the field and so the flux through the coil is changing with time, in a periodic (sinusoidal) way. As a result an emf is induced in the coil, which is also varying, that, by Lenz's law, opposes the change in flux, i.e., the rotation; we refer to it as a "back-emf". That means the current induced in the coil will be opposite to the current causing the rotation in the first place! So, the induced current actually tends to slow the motor down but, of course, normally it is overcome by the motor drawing "extra" current from the electrical supply. If the current to the coil is switched off by simply opening the circuit then, not only is the current in the coil reduced to zero so there is no magnetic moment and, hence, no torque and no drive, but there is now no "back-current" either. Yes, there is a "back-emf" in the coil - because it's still rotating - but no current flows because the coil is open circuit with infinite resistance. On the other hand, if the supply current is switched off but the coil remains part of a complete circuit, then the induced emf will produce a current that opposes the change in flux and since there is no current from the supply the motor will stop rather quickly. So, the magnetic field, the coil and an induced current combine to act as a "brake".

I've shown above how a double-pole switch could connect the coil to a supply when in one direction ("ON") and produce a "short" when switched in the other direction ("OFF"). In the off position the ends of the coil are simply connected to each other so a complete circuit is formed.

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