A changing magnetic flux

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

    A circular wire loop of radius r= 19 cm is immersed in a uniform magnetic field B= 0.670 T with its plane normal to the direction of the field.


    If the field magnitude then decreases at a constant rate of −1.2×10−2 , at what rate should increase so that the induced emf within the loop is zero?

    2. Relevant equations

    Basically the most relevant equation is:

    -(dɸ)/(dt)=Emf

    3. The attempt at a solution

    I'm not too sure how to attempt this problem. It would be greatly appreciated if someone could get me started.

    -Melqarthos
     
  2. jcsd
  3. At what rate should what increase? The radius? or just the area of the wire?

    In order for the induced EMF to be zero, -(dɸ)/(dt) = 0. ɸ = B*Area if the field is perpendicular to the loop. You have dB/dt by the problem statement, so you should be able to solve for dA/dt and dr/dt using geometric relations. Also note that when you differentiate the flux, that both the area and the magnetic field are time-dependent.
     
  4. What do you mean by geometric relations? I'm not quite sure.
     
  5. Never mind. I got it. we just use this relationship:

    (dΦ)/(dt)=(BcosΘ)(dA/dt)+(AcosΘ)(dB/dt) + AB(-sinΘ)(dΘ/dt), in which case the last term is equal to zero as the angle does not change. Only the magnitude and area change.

    Thanks!

    Melqarthos
     
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