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The current density acrossa cylindrical conductor of radius R varies according to the equation J=J0 [ 1-r/R], where r=distance from the axis. Thus the current density is maximum J0 at the axis r=0 and decreases linearly to zero at the surface r=R.Calculate the current in terms of J0 and the conductor's cross-sectional area A= pi R2 .
Supppose that instead the current density is a maximum J0 at the surface and decreases linearly to zero at the axis so that J=J0 r/R. Calculate the current.
Hi
J=J0 [ 1-r/R] I= ∫ JdA from 0 to R dA=2pi*rdr considering it is a cylinder, so consider a ring element and hence the differntial area would come out to be this.... On integrating we get I=J0*pi*R2/3 Similarly integrate JdA for the other case to get I. ITs is exactly the same, just the J term needs to be changed in the integration.
I= ∫ JdA from 0 to R
On integrating we get I=J0*pi*R2/3
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