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Grade: Upto college level
        

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.

10 years ago

Answers : (1)

AskiitianExpert Shine
10 Points
							

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.

10 years ago
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