A uniform magnetic field of 7.35 T points in some direction. Consider the magnetic flux through a large triangular wire loop that has three

Question

A uniform magnetic field of 7.35 T points in some direction. Consider the magnetic flux through a large triangular wire loop that has three equal sides of 1.95 m. Determine the maximum of the absolute value of the magnetic flux.

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Delwyn 5 years 2021-08-12T21:02:59+00:00 1 Answers 9 views 0

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  1. Nem
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    2021-08-12T21:04:55+00:00
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    Answer:

    The  maximum of the absolute value of the magnetic flux is \phi_{max} = 12.10 1 \ Weber

    Explanation:

    From the question we are told that

        The magnetic field is B = 7.35 \ T

       One  side of the triangle  is  d = 1.95 \ m

    Generally the  absolute value of the magnetic flux is mathematically represented as

             \phi = B * A cos (\theta _1 )

    At maximum  \theta_1 = 0

    So

    The maximum of the absolute value of the magnetic flux.

                \phi_{max} = B * A

    Now we are told that the triangle is of equal sides so the angle each makes with the other is  \theta = 60 ^o this is because total angle in a triangle is 180

       Now the height of the triangular loop is mathematically evaluated using SOHCAHTOA  as

             sin \theta =\frac{h}{d}

    =>    sin( 60)=\frac{h}{1.95}

    =>    h = sin (60) * 1.95

    =>    h = 1.6887 \ m

    Hence the area is evaluated as

         A = \frac{1}{2} * d * h

    substituting values

         A = 0.5 * 1.95 * 1.6887

         A = 1.6465 \ m^2

    Thus  

           \phi_{max} = 7.35 * 1.6465

           \phi_{max} = 12.10 1 \ Weber

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