(a) A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil? (b) Is this number of turns of wire practical for a 1.00 by 3.00 cm coil?
Question by OpenStax is licensed under CC BY 4.0
Final Answer
  1. 50 turns
  2. Yes, 50 turns of thin wire can easily be wrapped in a coil of this size.

Solution video

OpenStax College Physics for AP® Courses, Chapter 23, Problem 32 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A bicycle generator has an angular velocity of 1875 radians per second, a peak voltage of 18.0 volts, the coil is square shaped with a length of 1.00 centimeter and a width of 3.00 centimeters and I convert those into meters and then the magnetic field of this magnet inside the generator is 0.640 tesla. So I have the letter w here and the letter ω up here and then hope there's no confusion; I am trying to distinguish them by having a sort of pointy peaks on this w and this one is a scripted sort of curvy w. Okay! So we are going to figure out the number of turns in this coil so peak voltage is the number of turns times the area of the coil times the magnetic field strength times the angular velocity and since it's a rectangular shaped coil, the area is the length multiplied by the width and so we substitute that in place of letter A and then we solve for the number of turns N by dividing both sides by lwBω. Okay! So the number of turns then is the peak voltage of 18.0 volts divided by 1.00 times 10 to the minus 2 meters length and then multiply that by 3.00 times 10 to the minus 2 meters— width of the coil— times 0.640 tesla times 1875 radians per second and that works out to 50 turns. And 50 turns is realistic for a coil of this size given some thin wire so part (b) our answer is yes, you can have 50 turns.