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.

Answer 1

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  

       $\phi_{max} = 7.35 * 1.6465$

       $\phi_{max} = 12.10 1 \ Weber$