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Show that the dimensions of the displace...

Show that the dimensions of the displacement current `(omega_0(d Phi_E)/dt)` are that of an electric current.

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The displacement current is

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Knowledge Check

  • Dimension of electric current is

    A
    `[M^(0)L^(0)T^(-1)Q]`
    B
    `[ML^(2)T^(-1)Q]`
    C
    `[M^(2)LT^(-1)Q]`
    D
    `[M^(2)L^(2)T^(-1)Q]`

  • Displacement current I_(D) is given as

    A
    `I_(D)=in_(0)(dphi_(E))/(dt)`
    B
    `I_(D)=mu_(0)(dphi_(E))/(dt)`
    C
    `I_(D)=(1)/(in_(0))(dphi_(E))/(dt)`
    D
    `I_(D)=(1)/(mu_(0))(dphi_(B))/(dt)`

  • Dimensions of epsi_(0) (dphi_(E))/(dt) are same as that of

    A
    charge
    B
    potential
    C
    capacitance
    D
    current

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    Why is the quantity in_0(dphi_E)/(dt) called the displacement current? Where dphi_E//dt is the rate of change of electric flux linked with a region or space.

    A long straight cable of length l is placed symmetrically along z-axis and has radius a(ltlt l). The cable consists of a thin wire and a co- axial conducting tube. An alternating current I(t) = I_(0) " sin " (2pi vt) . Flows down the central thin wire and returns along the co-axial conducting tube. the induced electric at a distance s from the wire inside the cable is E(s ,t) =mu_(0) I_(0) v " cos "(2pivt) In ((s)/(a)) hatk . (i) Calculate the displacement current density inside the cable. (ii) Integrate the displacement current density across the cross- section of the cable to find the total displacement current I^(d) . (iii) compare the conduction current I_(0) with the displacement current I_(0)^(d) .

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