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A closely wound rectangular coil of 100 turns has dimensions of 27.0 cm by 50.0 cm . The plane of the coil is rotated from a position where it makes an angle of 37.0 ∘ with a magnetic field of 1.20 T to a position perpendicular to the field. The rotation takes 9.00×10−2 s . (Note that the coil is perpendicular to the area vector of the coil.) What is the average EMF induced in the coil?

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Answer:

[tex]\epsilon =71.677V[/tex] induced.

Explanation:

We define all our variables,

[tex]B=1.2T[/tex]

[tex]A=0.27m*0.50m[/tex]

[tex]\theta= 90-37[/tex]

[tex]\Delta T= 0.09s[/tex]

[tex]N= 100[/tex]

EMF induced is given through the expression

[tex]\epsilon = \frac{-N\Delta \Phi}{\Delta t}[/tex]

Here we understand [tex]\Phi[/tex] as

[tex]\Phi = BAcos\theta[/tex]

We proceed to calculate the entire Initial Flow as the final, as well

[tex]\Phi_i=(1.2)(0.27*0.5)cos(90-37) = 0.09749Tm^2[/tex]

Final Flow

[tex]\Phi_f=(1.2)(0.27*0.5)= 0.162Tm^2[/tex]

Now, if [tex]\Delta t = 0.09s[/tex],

[tex]\epsilon= (100)(0.162Tm^2 - 0.09749Tm^2)/(0.09s)[/tex]

[tex]\epsilon =71.677V[/tex] induced.

NOTES:

  • It is necessary to make two small notes regarding the development of the exercise. The subtraction of the angles is used since the exercise indicates that the angle is between the field B and the Plane. However, the measurement between the Area and the field is required b.
  • Negative signs can be neglected because it is understood that this is a reference to know which direction has the highest potential.

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