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प्रश्न
Show that the dimensions of the displacement current `∈_0 (d varphi_E)/dt` are that of an electric current .
उत्तर
Displacement current,
`I_D = (∈_0 d varphi_e)/dt`
Electric flux,
`Ø_e = EA`
`[Ø_e] = [E] [A]`
= `[1/(4pi∈_0) q/r^2] [A]`
Also , `[∈_0] = [M^-1L^-3 T^4 A^2]`
⇒ `[Ø_e] = [M^1L^3T^-4A^-2] [AT][L^-2][L^2]`
= `[ML^3T^-3A^-1]`
Displacement current,
`[I_D] = [∈_0] [Ø_e] [T^-1]`
`[I_D] = [M^-1L^-3T^4A^2] [ML^3T^-3A^-1][T^-1]`
`[I_D] = [A]`
`[I_D] = ["Current"]`
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