Question

segment BC is an are of a circle with radius 30.0 cm, and point P is at the center of curvature of the arc Segment DA is an arc of a circle with radius 20.0 cm, and point P is at its center of curvature. Segments CD and AB are straight lines of length 10.0 cm each. Calculate the magnitude of the magnetic field at a point P due to a current 11.4 A in the wire. Express your answer with the appropriate units. What is the direction of magnetic field? into the page out of the page

Answer 1

Answer:

The magnetic field is $B = 3.87 *10^{-6} \ T$

Direction is inward

 

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image  

From the question we are told that

      The radius of  BC is  $r_{BC} = 30 \ cm = 0.30 \ m$

      The radius of  DA is $r _{DA} = 20 \ cm = 0.20 \ m$

      The length of CD is  $r_{CD} = 10 cm = 0.1 \ m$

      The length of AB is  $r_{AB} = 10 cm = 0.1 \ m$

      The current is  $I = 11.4A$

The magnetic field is mathematically represented as

      $B = B_{BC} + B_{DA} + B_{CD} + B_{AB}$

       $B = \frac{\mu_o I}{4 \pi } [ \frac{\theta_{DA}}{r_{DA}} + \frac{\theta_{BC}}{r_{BC}}+ \frac{\theta_{CD}}{r_{CD}}+\frac{\theta_{AB}}{r_{AB}}]$

        Where

                 $\theta_{BC} = \theta_{DA} = \frac{2\pi}{3}$

Where  $\frac{2 \pi}{3} = 120^o$

                $\theta_{CD} = \theta_{AB} = 0^o$

so

        $B = \frac{\mu_o I}{4 \pi } [ \frac{\frac{2\pi}{3} }{0.20} - \frac{\frac{2\pi}{3}}{0.30}}+ \frac{0}{0.10}+\frac{0}{0.10}]$

         $B = 3.87 *10^{-6} \ T$

The direction is into the page

    This because the magnitude of the magnetic field due to arc BC whose direction is outward is less than that of DA whose direction is inward

This is because according to Fleming's Left Hand Rule  the direction of current is perpendicular to the direction of magnetic field so since  current in arc BC and DA are moving in opposite direction their magnetic field will also be moving in opposite direction