(a) A nonferrous screwdriver is being used in a 2.00 T magnetic field. What maximum emf can be induced along its 12.0 cm length when it moves at 6.00 m/s? (b) Is it likely that this emf will have any consequences or even be noticed?
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Final Answer
  1. 1.44 V1.44\textrm{ V}
  2. This is approximately the voltage of a AA battery. It is unlikely to be noticed. One can touch the terminals of a AA battery without noticing any effect.

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 18 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A non-ferrous screwdriver, which is to say a screwdriver that is not made out of iron and therefore not steel is moving with a speed of 6.00 meters per second through a magnetic field with a strength of 2.00 tesla and the length of this screwdriver is 12.0 centimeters, which is 12.0 times 10 to the minus 2 meters. The question (a) is asking us for the maximum possible induced voltage along its length and that will occur when you have the velocity perpendicular to the length because you want to maximize the amount of length perpendicular to the velocity in order to maximize the emf that's induced. And the reason for that is that the loose charges that are in this metal are going to have a force exerted on them when they move through this magnetic field and the amount of work that that force does on those charges separating them on one end versus the other is therefore the electric potential; that work done becomes the potential energy of those charges when they are separated and so the greater distance over which that occurs, the more the potential. So the formula for this emf is the magnetic field strength times the length of the screwdriver times its speed so that's 2.00 tesla times 12.0 times 10 to the minus 2 meters times 6.00 meters per second and that's 1.44 volts. And this is approximately the voltage of a AA battery and so it's unlikely to be noticed because you can touch the terminals of a AA battery and you will have no ill effect and it doesn't you know usually cause any problems; if you put your tongue on a 9 volt battery then you can begin to feel the effect of a battery... you know, type voltage but a AA battery is much smaller than that, it's only one and a half volts.