Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Coil length or Solenoid length?

  1. Apr 18, 2010 #1
    This is not a homework. I am just pretty confused about a problem (with solution!) I saw in the internet found here:

    The part I am confused is the mutual inductance part. Here I repeat the question:

    1. The problem statement, all variables and given/known data
    A long solenoid of length 1 m, cross sectional area 10 cm2, having 1000 turns has wound about its centre a small coil of 20 turns. Compute the mutual inductance of the two circuits. What is the emf in the coil when the current in the solenoid changes at the rate of 10 Amp/s?

    2. Relevant equations

    I am assuming in the question, both coils are wound such that both has the same coil length as the solenoid.

    3. The attempt at a solution

    The mutual inductance [tex]M[/tex] is given as:

    M = \frac{\mu N_1 N_2 I_2 A}{l}

    where [tex]l[/tex] is the length is the solenoid length. Suppose the 20 turns coil has shorter coil length. Would that affect the mutual inductance value?
  2. jcsd
  3. Apr 18, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. As long as the coil is near the midpoint of the solenoid and its ends do not extend very far from the midpoint, the length of the coil does not matter much. This is an approximate calculation which assumes that the magnetic field generated by the solenoid is uniform at the location of the coil. It is most accurate at the solenoid's midpoint. As you move the coil closer to the ends of the solenoid, the field generated by the solenoid is less and less uniform which makes the approximation less and less valid.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook