Answer:
The induced emf is [tex]\epsilon = 0.0280 \ V[/tex]
Explanation:
From the question we are told
  The diameter of the loop is  [tex]d = 6.7 cm = 0.067 \ m[/tex]
  The magnetic field is  [tex]B = 1.27 \ T[/tex]
  The time taken is  [tex]dt = 0.16 \ s[/tex]
Generally the induced emf is mathematically represented as
     [tex]\epsilon = - N * \frac{\Delta \phi}{dt}[/tex]
Where  N =  1 given that it is only a circular loop
      [tex]\Delta \phi = \Delta B * A[/tex]
Where  [tex]\Delta B = B_f - B_i[/tex]
  where [tex]B_i[/tex] is  1.27 T  given that the loop of wire was initially in the magnetic field
  and  [tex]B_f[/tex] is  0 T given that the loop was removed from the magnetic field
Now the area of the of the loop is evaluated as
     [tex]A = \pi r^2[/tex]
Where r is the radius which is mathematically represented as
    [tex]r = \frac{d}{2}[/tex]
substituting values
    [tex]r = \frac{0.067}{2}[/tex]
    [tex]r = 0.0335 \ m[/tex]
So
     [tex]A = 3.142 * (0.0335)^2[/tex]
     [tex]A = 0.00353 \ m^2[/tex]
So
   [tex]\Delta \phi = (0- 127)* (0.00353)[/tex]
   [tex]\Delta \phi = -0.00448 Weber[/tex]
=> Â Â [tex]\epsilon = - 1 * \frac{-0.00448}{0.16}[/tex]
=> Â [tex]\epsilon = 0.0280 \ V[/tex]
