Question

A tightly wound toroid of inner radius 1.2 cm and outer radius 2.4 cm has 960 turns of wire and carries a current of 2.5 A.

Answer 1

Answer:

a

  $B = 0.0533 \ T$

b

  $B = 0.04 \ T$

Explanation:

From the question we are told that

   The inner radius is $r = 1.2 \ cm = 0.012 \ m$

   The  outer radius is  $r_o = 2.4 \ cm = \frac{2.4}{100} = 0.024 \ m$

    The nu umber of turns is  $N = 960$

    The current it is carrying is  $I = 2. 5 A$

Generally the magnetic field is mathematically represented as

      $B = \frac{\mu_o * N* I }{2 * \pi * r }$

Where  $\mu_o$ is the permeability of free space with a constant value    

            $\mu = 4\pi * 10^{-7} N/A^2$

And the given distance where the magnetic field is felt is  r =  0.9 cm  =  0.009 m

Now  substituting values

     $B = \frac{ 4\pi * 10^{-7} * 960* 2.5 }{2 * 3.142 * 0.009 }$

    $B = 0.0533 \ T$

    Fro the second question the distance of the position considered from the center is  r =  1.2 cm  =  0.012 m

So the  magnetic field is  

        $B = \frac{ 4\pi * 10^{-7} * 960* 2.5 }{2 * 3.142 * 0.012 }$

        $B = 0.04 \ T$