The current density in a conducting medium is given by J → = 40 ρ 2 + 1 a z ^ m A / m 2 .The net current crossing the circular disc ( 0 &lt; ρ &lt; 5 m ) in z = 2 plane is _____mA.1)409.42 2)40.94 3)904.42 4)90.44

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The current density in a conducting medium is given by       J    →    =      40                  ρ        2            +      1                          a                  z                    ^        m  A      /        m    2  .The net current crossing the circular disc   (  0  &amp;lt;  ρ  &amp;lt;  5  m  ) in z = 2 plane is _____mA.1)409.42 2)40.94 3)904.42 4)90.44

Ludvikqqg · Accepted Answer

The first option is correct 409.42We have,   I  =      ∫          s            J    →    ∗            d      s        →    =      ∫          ϕ      =      0              2      π            ∫          0              5            40                  p                  2                    +      1        d  ρ  d  ϕ  m  A  =  80  π      ∫          0              5            ρ                  ρ                  2                    +      1        d  ρ  d  ϕ  m  A  =            80      π        2    ln  ⁡  (      ρ          2        +  1  )            |              0              5        m  A  =  40  π  [  ln  ⁡  (  26  )  −  ln  ⁡  (  1  )  ]  =  40  π  ×  3.258  =  409.42  m  A

The current density in a conducting medium is given by vec J=(40)/(rho^2 +1)hat(a_z)mA/m^2 The net current crossing the circular disc (0< rho < 5m) in z = 2 plane is _____mA. 1)409.42 2)40.94 3)904.42 4)90.44

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