a) The current density across a cylindrical conductor of radius R varies according tot he equation j = jo(1-r/R)(adsbygoogle = window.adsbygoogle || []).push({});

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

Thanks

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# Homework Help: Current and Current Density

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