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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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To calculate the current flowing through a cylindrical conductor with a varying current density, we can follow these steps: ### Step 1: Understand the Current Density Equation The current density \( J \) is given by the equation: \[ J = J_0 \left(1 - \frac{r}{R}\right) \] where: ...
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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.

Suppose that instead the current density is a maximum J_(0) at the surface and decreases linearly to zero at the axis so that J=J_(0)(r )/(R ) . Calculate the current.

Knowledge Check

  • 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

  • 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 conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field, B with the distance, d from the centre of the conductor, is correctly represented by the figure

    A
    B
    C
    D

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