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Homework Help: Inductive Heater

  1. May 16, 2015 #1
    1. The problem statement, all variables and given/known data

    A 34.6 -cm-diameter coil consists of 25 turns of circular copper wire 2.25 mm in diameter. A uniform magnetic field, perpendicular to the plane of the coil, changes at a rate of 3.55 × 10-3T/s. Determine

    a. the current I in the loop,

    b. and the rate dU/dt at which thermal energy is produced.

    2. Relevant equations

    magnetic flux = B*A cos Theta

    I = magnetic flux / R

    R = p (L/A) where p is the resistivity of copper

    3. The attempt at a solution

    Here is what I attempted:

    First, I found the magnetic flux by using the formula: B*A cos Theta

    multiplying the area by 25 because it's in a coil and using .173 meters for the radius of the coil

    (3.55*10^-3)(25*.173) = 1.535375*10^-2

    then to find I (current) :

    I = magnetic flux / resistance

    I calculated resistance by :

    since it's a coil, I multiplied the L by 25 and the A by 25

    R = p (L/A) = 1.68*10^-8 (25*pi*.173 / 25*pi*1.125*10^-2)^2 = 0.001148

    plugging in that into the I equation, I = 1.535375e-2 / 0.001148 = 13.374 A

    This isn't the right answer and I messed something up. I would appreciate if someone could help me with catching my mistake! I appreciate it!

    Thanks in advance!
  2. jcsd
  3. May 16, 2015 #2
    again. why do you say that i=magnetic flux/R ?
    so i is the change in magnetic flux per unit time/R.
    what is the area of cross section of wire?
  4. May 16, 2015 #3
    I meant to say that i = emf/R

    The area of the cross section is pi*r^2 which is pi(.00225)^2 where .00225 is the radius of the wire

    = 1.590431e-5

    Would I only multiply the circumference of the coil by 25?
  5. May 16, 2015 #4
    no. 2.25 is its diameter.
  6. May 16, 2015 #5
    Oh that's right! My bad.

    R = p (L/A) = 1.68*10^-8 (25*pi*.173 / pi*(0.00225/2)^2 = .11482

    then I = Emf/R = B*Area of coil / R = 3.41194*10^-2 / .11482 = 0.297155 A

    Still not getting it right. When calculating for the Emf, did I do that right? or is the fact that i's a changing magnetic field need some different calculation to get the Emf?
  7. May 17, 2015 #6
    what is the total length of wire? your value of L in R=p(LA) is wrong.
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