Question

Point PP is a distance d1d1 = 4.0 mm above a large sheet of metal that carries a current of 35 AA in the positive xx direction and a distance d2d2 = 3.0 mm below a very long wire that carries a current of 0.41 AA in the positive xx direction. If the magnetic field magnitude at P is zero, calculate the width of the metal sheet.

Answer 1

Answer:

The width of the sheet is   $w =0.8046m$

Explanation:

  From the question we are told that

             The distance of point P above a  large sheet of metal is $D = 4.0mm =\frac{4}{1000} = 0.004m$

             The current on the large metal sheet  is  $I =34A$

              The  distance of the the point P below a long wire $d = 3.0mm = \frac{3}{1000} = 0.003m$

               The current on the long wire is  $I_w = 0.41A$

                The magnetic field at  P is  $B = 0T$

Generally magnetic field  of P long wire is mathematically represented as

                $B_w = \frac{\mu_o I_w}{2\pi r}$

Generally magnetic field  of P large sheet of meta is mathematically represented as

              $B_m = \frac{\mu_o K}{2}$

Where K is the current per unit width

 The total magnetic field at P is

                  $\frac{\mu_o I_w}{2 \pi r} = \frac{\mu_o K}{2}$

Making K the subject of formula

                 $K = \frac{2 I_w }{2 \pi r }$

 Substituting values

                   $K = \frac{2 * 0.41 }{2 * 3.142 * (0.0030) }$

                        $K = 43.4967 A/m$

Generally K is mathematically represented as

                $K = \frac{I}{w}$

Where w is the width of the large sheet

Therefore the width  of the metal sheet   $w = \frac{I}{K}$

                                                                         $= \frac{35}{43.4967}$

                                                                         $w =0.8046m$