A circular conducting loop of radius 25.0 cm is located in a region of homogeneo

Question

A circular conducting loop of radius 25.0 cm is located in a region of homogeneous magnetic field of magnitude 0.500 T pointing perpendicular to the plane of the loop. The loop is connected in series with a resistor of 121 . The magnetic field is now increased at a constant rate by a factor of 2.80 in 31.0s.
Calculate the magnitude of the induced emf in the loop while the magnetic field is increasing.

Calculate the magnitude of the current induced in the loop while the field is increasing.

With the magnetic field held constant at its new value of 1.40 T, calculate the magnitude of the average induced voltage in the loop while it is pulled horizontally out of the magnetic field region during a time interval of 5.90 s.

Explanation / Answer

The area of the loop is:

A = r²

   = * (0.25 m)²   = 0.19625 m²

The change in magnetic flux is:

= AB  

       = 0.19625 m² * ((2.8 * 0.5T) - 0.5 T)

       = 0.1766 Wb

A)    The induced emf is:

       E = / t

         = 0.1766 Wb / 31 s

         =   5.696   mV

B)   the magnitude of the current induced in the loop = 5.696 / 121

                                                                                     =   0.047 mA

C)    The change in magnetic flux is:

       = AB

            = 0.19625 m² * (0 T - 1.40 T)

             = - 0.27475 Wb

    The average induced emf:

     E = - / t  

        = 0.27475 Wb / 5.90 s

        =   46.567 mV

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