Question

The magnetic coils of a tokamak fusion reactor are in the shape of a toroid having an inner radius of 0.700 m and an outer radius of 1.20 m. The toroid has 900 turns of large diameter wire, each of which carries a current of 13.0 kA. Find the difference in magnitudes of the magnetic fields of the toroid along the inner and outer radii. (Enter your answer in T.)

Answer 1

Answer:

The difference is $\Delta B = 1.39 \ T$

Explanation:

From the question we are told that  

    The inner radius  is  $r_i = 0.700 \ m$

        The outer radius  is  $r_o = 1.20 \ m$

        The number of turns is  $N = 900 \ turns$

        The current on each wire is $I = 13.0 kA = 13*10^{3} \ A$

Generally magnetic field of a toroid along the outer radius is mathematically evaluated as

        $B_o = \frac{\mu_o * N * I}{2 \pi r_o}$

Where  $\mu_o$ is the permeability of free space with value $\mu_o= 4\pi * 10^{-7} N/A^2$

substituting values

            $B_o = \frac{ 4\pi * 10^{-7} * 13*10^{3} * 900}{ 2 * 3.142 * 1.20}$

           $B_o = 1.95 \ T$

Generally magnetic field of a toroid along the inner radius is mathematically evaluated as

           $B_i = \frac{\mu_o * N * I}{2 \pi r_i}$

substituting values

           $B_i = \frac{ 4\pi * 10^{-7} * 900 * 13*10^{3}}{2 *3.142 *0.700}$

         $B_i = 3.34 \ T$

The difference in  magnitudes of the magnetic fields of the toroid along the inner and outer radii is mathematically evaluated as

      $\Delta B = B_i - B_o$

      $\Delta B = 3.34 -1.95$

      $\Delta B = 1.39 \ T$