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The current density across a cylindrical...

The current density across a cylindrical conductor of radius `R` varies in magnitude according to the equation `J = J_0(1 - (r )/(R ))` where `r` is the distance from the central axis. Thus, the current density is a maximum `J_0` at that axis `(r = 0)` and decreases linearly to zero at the surface `(r = R)`. Calculate the current in terms of `J_0` and the conductor's cross - sectional area `A = piR^2`.

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Knowledge Check

  • The current density varies radical distance r as J=ar^(2) , in a cylindrical wire of radius R. The current passing through the wire between radical distance R//3 and R//2 is,

    A
    `(65piaR^(4))/(2592)`
    B
    `(25piaR^(4))/(72)`
    C
    `(65pia^(2)R^(3))/(2938)`
    D
    `(81pia^(2)R^(4))/(144)`

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