Question

A -turn rectangular coil with length and width is in a region with its axis initially aligned to a horizontally directed uniform magnetic field of mT and set to rotate about a vertical axis with an angular speed of rad/s. What is the maximum induced emf in the rotating coil? What is the induced emf in the rotating coil at ? What is the maximum rate of change of the magnetic flux through the rotating coil?

Answer 1

Complete Question

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Answer:

The maximum emf is $\epsilon_{max}= 26.8 V$

The emf induced at t = 1.00 s is $\epsilon = 24.1V$

The maximum rate of change of magnetic flux is   $\frac{d \o}{dt}|_{max} =26.8V$

Explanation:

    From the question we are told that

        The number of turns is N = 44 turns

          The length of the coil is  $l = 15.0 cm = \frac{15}{100} = 0.15m$

          The width of the coil is  $w = 8.50 cm =\frac{8.50}{100} =0.085 m$

          The magnetic field is  $B = 745 \ mT$

          The angular speed is $w = 64.0 rad/s$

Generally the induced emf is mathematically represented as

        $\epsilon = \epsilon_{max} sin (wt)$

 Where $\epsilon_{max}$ is the maximum induced emf and this is mathematically represented as

            $\epsilon_{max} = N\ B\ A\ w$

Where $\o$ is the magnetic flux

            N is the number of turns

             A is the area of the coil which is mathematically evaluated as

             $A = l *w$

        Substituting values

           $A = 0.15 * 0.085$

               $= 0.01275m^2$

substituting values into the equation for  maximum induced emf

         $\epsilon_{max} = 44* 745 *10^{-3} * 0.01275 * 64.0$

                 $\epsilon_{max}= 26.8 V$

 given that the time t = 1.0sec

substituting values into the equation for induced emf  $\epsilon = \epsilon_{max} sin (wt)$

      $\epsilon = 26.8 sin (64 * 1)$

        $\epsilon = 24.1V$

   The maximum induced emf can also be represented mathematically as

              $\epsilon_{max} = \frac{d \o}{dt}|_{max}$

  Where  $\o$ is the magnetic flux and $\frac{d \o}{dt}|_{max}$ is the maximum rate at which magnetic flux changes the value of the maximum rate of change of magnetic flux is

         $\frac{d \o}{dt}|_{max} =26.8V$