# Current and Current Density

1. Feb 24, 2008

### Destrio

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

Thanks

2. Feb 24, 2008

### Destrio

anyone?

3. Feb 26, 2008

### STellY

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