Question

A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm>s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. (a) Find the emf induced in the

Answer 1

Answer:

emf = - 0.622 V

Explanation:

The electromotive force is given by Faraday's law

         emf = $- \frac{d \phi }{dt}$

         Ф = B. A

bold indicates vectors

        Ф = B A cos θ

in this case it is indicated that the magnetic field is constant and the angle between the magnetic field and the normal to the area is parallel, so the cos 0 = 1

       

we substitute

           emf = $- B \ \frac{dA}{dt}$

the area of ​​the circle is

          A = pi r²

         $\frac{dA}{dt} = \pi 2r \ \frac{dr}{dt}$

       emf = B 2π r $\frac{dr}{dt}$

speed is defined

       v = $\frac{dr}{dt}$

         

we substitute

        emf = - 2π B r v

let's calculate

        emf = - 2π  0.5  1.65  π0.12

        emf = - 0.622 V