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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 surface `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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`J_(0)A//3`,
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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 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
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    C
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    D
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  • 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
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