If a single circular loop of wire carries a current of 61 A and produces a magnetic field at its center with a magnitude of 1.70 10-4 T, determine the radius of the loop.

Respuesta :

Answer:

The  radius is  [tex]R = 0.22 5 \ m[/tex]

Explanation:

From the question we are told that

    The current is  [tex]I = 61 \ A[/tex]

     The  magnetic field is  [tex]B = 1.70 *10^{-4} \ T[/tex]

Generally the magnetic field produced by a current carrying conductor  is mathematically represented as

        [tex]B = \frac{\mu_o * I}{2 * R }[/tex]

=>     [tex]R = \frac{\mu_o * I }{ 2 * B }[/tex]

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

=>    [tex]R = \frac{ 4\pi * 10^{-7} * 61 }{ 2 * 1.70 *10^{-4} }[/tex]

=>  [tex]R = 0.22 5 \ m[/tex]