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State the modified Ampere's circuital la...

State the modified Ampere's circuital law.

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Ampere-Maxwell law (modified Ampere's circuital law): Ampere's circuital law modified by Maxwell for a time-varying current states that in free space the line intergral of magnetic induction around a closed path in a magnetic field is equal to `mu_0` times the net steady current through a surface enclosed by the path and a contribution due to the changing electric flux arising from the time-varying current. In mathematical form.
`ointvecB.vec(dl)=mu_0(I_c+epsi_0(dphi_e)/(dt))`
Where `vecB` is the magnetic induction at any point on the path, `vec(dl)` is the length element of the path, `mu_0` is the permeability of free space. `I_c` is the total conduction current through a surface enclosed by the closed path and `I_d=epsi_0(dphi_e)/(dt)` is the fictitious displacement current arising from the changing electric flux `phi_e`.
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Knowledge Check

  • Which one of the following equations represents the modified from of Ampere's circuital law?

    A
    `oint vec(B) cdot d vec(s)=mu_(0)I`
    B
    `oint vec(B) cdot d vec(l)=mu_(0)I`
    C
    `oint vec(B) cdot d vec(l)=mu_(0)[I+epsilon_(0)(d phi_(E))/(dt)]`
    D
    `oint vec(B) cdot d vec(l)=mu_(0)I+1/(mu_(0)epsilon_(0))(d phi_(E))/(dt)`
  • Maxwell's modified form of Ampere's circuital law is

    A
    `ointvecB.vec(ds)=0`
    B
    `ointvecB.vec(dl)=mu_(0)I`
    C
    `ointvecB.vec(dl)=mu_(0)I+(1)/(epsilon_(o))(dq)/(dt)`
    D
    `ointvecB.vec(dl)=mu_(0)I+mu_(0)epsilon_(o)(d oint_(E))/(dt)`
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