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The current density in a cylindrical con...

The current density in a cylindrical conductor of radius R varies according to the equation `J=J_(0)(1-r/R)`, where r=distacnce from the axis. Thus the current density is a maximum `J_(0)` ata the axis r=0 and decreases linealy to zero at the srface `r=2/sqrtpi`. Current in terms of `J_(0)` is given by `n(J_(0)/6)` then value of n will be.

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Knowledge Check

  • The current density in a wire of radius a varies with radial distance r as J=(J_0r^2)/a , where J_0 is a constant. Choose the incorrect statement.

    A
    Total current passing through the cross-section of the wire is`I=(piJ_0a^3)/2`
    B
    Total current passing through the cross-section of the wire is`I=(3piJ_0a^3)/2`
    C
    The field at a distance r gt a is `B=(mu_0J_0a^3)/(4r)`
    D
    The field at a distance r gt a is `B=(mu_0J_0a^3)/(4a)`

  • The current density is a solid cylindrical wire a radius R, as a function of radial distance r is given by J(r )=J_(0)(1-(r )/(R )) . The total current in the radial regon r = 0 to r=(R )/(4) will be :

    A
    `(5J_(0)pi R^(2))/(32)`
    B
    `(5J_(0)piR^(2))/(96)`
    C
    `(3J_(0)piR^(2))/(64)`
    D
    `(J_(0)piR^(3))/(128)`

  • A cylindrical wire of radius R has current density varying with distance r form its axis as J(x)=J_0(1-(r^2)/(R^2)) . The total current through the wire is

    A
    `(piJ_0R^2)/2`
    B
    `(2piJ_0R^2)/3`
    C
    `(4piJ_0R^2)/3`
    D
    none of these
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