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Homework Help: Current and Current Density

  1. Feb 24, 2008 #1
    a) The current density across a cylindrical conductor of radius R varies according tot he equation j = jo(1-r/R)
    where r is the distance from the axis. Thus the current density is a maximum jo at the axis r=0 and decreases linearly to zero at the surface r=R. Calculate the current in terms of jo and the conductor's cross sectional area A = piR^2

    so i took i = integral from 0 to R of jdA
    i = jopiR^2(r-r^2/2R) |(0,R)
    i = jopiR^2(R-(R/2) = (1/2)jopiR^3

    b) Suppose that instead the current density is a maximum jo at the surface and decreases linearly to zero on the axis, so that
    j = jor/R

    so i did the same thing and got
    i=jopiR(R^2/2) = (1/2)jopiR^3

    Why is the result different from a?
    I realized at this point in the question that I must have made a mistake, as I got the same result from b as i did in a

  2. jcsd
  3. Feb 24, 2008 #2
  4. Feb 26, 2008 #3
    You may want to try making dA an infinitesimal ring so that dA = 2(Pi)(r)(dr) I believe you will get something like 1/2 and 1/6 R^2
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