Question

A long, straight wire of radius R carries a steady current I that is uniformly distributed through the cross section of the wire. Calculate the magnetic field a distance r from the center of the wire in regions r ≥ R and r < R.

Answer 1

Answer:

a

  When $r \ge R$

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

b

 When $r< R$

   $B = [\frac{\mu_o * I }{ 2 \pi R^2} ]* r$

Explanation:

From the question we are told that

   The  radius is  R  

   The  current is  I

    The  distance from the center

Ampere's law is mathematically represented as

       $B[2 \pi r] = \mu_o * \frac{I r^2 }{R^2 }$

      $B = \frac{ \mu_o}{2 \pi } * \frac{r}{R^2}$

When $r \ge R$

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

But when $r< R$

   $B = [\frac{\mu_o * I }{ 2 \pi R^2} ]* r$