Magnet and a Coil - induced current

  1. I am having difficulty on a conceptual question. I am thinking mastering physics is wrong here.



    1. The problem statement, all variables and given/known data

    When a magnet is plunged into a coil at speed , as shown in the figure, a voltage is induced in the coil and a current flows in the circuit.

    The same magnet is plunged into a coil that has twice the number of turns as before, as shown in the figure. (Part B 1 figure) If the speed of the magnet is again v, the induced current in the coil is _______ .


    A - twice as much
    B- four times as much
    C- half as much
    D - unchanged


    2. Relevant equations

    [​IMG]

    3. The attempt at a solution

    I answered with twice as much. which coincidentally the book on page 703 (college physics 8th edition) has this same example in it with the answer twice as much. Am I missing something? What answer do you get?

    Mastering Physics replied with this to my answer:
    Recall that the current in the coil is proportional to the induced emf, and inversely proportional to the resistance of the coil. Since the induced emf is proportional to the number of identical turns present in the coil, the induced voltage will be greater than that in the coil with fewer turns. How will the number of turns affect the resistance of the coil? Note that the turns in the coil are in series.


    Thanks
     
  2. jcsd
  3. alphysicist

    alphysicist 2,247
    Homework Helper

    Hi jcvince17,

    Are you sure the example in the book is not saying that the induced voltage is twice as much? The induced voltage is twice as much, but the question here is asking about the induced current. How is the induced current and voltage related?
     
  4. yes i do now.


    the voltage (EMF) is doubled. But as i see now the resistance is as well, doubled with the number of coils.

    therefore there is no change in current (I)

    :)
     
  5. The problem is not as easily aswered as implied.

    The problem consists of a magnet a coil and a meter. If the resistance of the meter is significantly greater than the resistance of the coil, then the measured current will approach twice the original measured current for the same magnet velocity.

    If the meter is considered to have no resistance then the observed current will remain the same if the diameter of the coil is held constant. As the circiut resistance is proportional to the linear length of wire.

    Vary the coil diameter leads to different answers. A coil with twice the turns and only half the diameter has the same resistance and the observed current will double in the case where the meter has no resistance.
     
  6. alphysicist

    alphysicist 2,247
    Homework Helper

    Hi StephenKen,

    Those facts are all true, but the further information that MasteringPhysics provided jcvince17 (in his original post) about the setup indicates that the meter is an ideal meter, and that the coil radius is unchanged.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?