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Write Maxwell’s generalization of Ampere...

Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process the current produced within the plates of the capacitor is
`i=epsilon_0(dPhi_E)/d_t`
where `Phi_E` is the electric. flux produced during charging of the capacitor plates.

Text Solution

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Electric field is along j-axis and magnetic field is along y-axis.

Ampere’s circuital law is given by
`phibarB.bar(dl)=mu_0I_e`
For a circuit containing capacitor, during its charging or discharging the current within the plates of the capacitor varies, producing displacement current ld. Hence, Ampere’s circuital law is generalised by Maxwell, given as
`phibarB.bar(dl)=mu_0I_e+mu_0I_e`
The electric flux `(phiF)` between the plates of capacitor changes with time, producing current within the plates which is proportional to. `(dphi_E)/(dt)` . Thus we get
`I_e=epsilon_0(dphi_epsilon)/(dt)`
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