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Homework Help: Emf induced in rotating coil

  1. Oct 6, 2009 #1
    1. The problem statement, all variables and given/known data

    A rectangular coil of 200 turns has a length of 200 mm and width
    120 mm. The coil rotates with a constant angular speed of 1200
    revolutions per minute about an axis through the midpoints of its
    longer sides in a uniform magnetic field of 2.4 x 10-2 T.

    Starting from a time when the coil’s plane is parallel to the
    magnetic field, calculate the average induced electromotive
    force whilst the coil is turning 1/(2pi) radians.

    2. Relevant equations

    E(emf) = N x B x w x A x sin (theta)
    where N = number of turns
    B = magnetic field (T)
    A = area of coil
    w = angular velocity (rad/s)
    theta = angle made by coil wrt perpendicular to the field

    3. The attempt at a solution

    Angular velocity = 40pi (1200rpm)

    As the coil rotates through the field plane the induced emf is at the maximum (sin (theta) = 1)
    E = 200 x 2.4 x 10-2 T x 40pi x 0.120m x 0.200m x sin (pi/2) = 14.47V

    After rotating towards the vertical through the rather small angle 1/(2pi) radians:
    E = 200 x 2.4 x 10-2T x 40pi x .120m x .200m x sin (pi/2 - (1/(2pi)) = 14.29V

    The given result is 9.216V so I've obviously missed something. Yet - it seems unusual that after rotating through such a small angle that the induced voltage should fall as low as the given answer.

    Help gratefully received!
  2. jcsd
  3. Oct 6, 2009 #2


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    Homework Helper

    if w=1200rpm why do you have 1200*40pi?
  4. Oct 6, 2009 #3
    I am not using 40pi * 1200: the rotational speed is 40pi which is used in the expression which requires angular velocity in rad/s. The 40pi comes from converting 1200rpm to rad/s. I then use the value 40pi for w (omega) in the expression..l.
  5. Oct 7, 2009 #4
    Comments anyone? Help and advice gratefully received... :)
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