a capacitor of capacitance "c" is being charged by connecting it across a dc source along with an ammeter .will the ammeter show a momentary deflaction during the process of charging?if so how would you explain this momentary deflection and resulting continuity of current in the circuit?write the expression for the current inside  the capacitor.

Yes the ammeter will shows a momentary deflection. And after some time (t = 5RC ) it move to zero when the capacitor gets fully charged. 

 Let the capacitor is charging with the help of resistance R.

Time constant of changing,

This is the expression for current at different time. 

i tends to zero  when t = 5RC 

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 When a capacitor is charged avery small current flows in the circuit due to which ammeter shows momentary deflection.

The continuity of current is explained by displacement current which is given by 

                                                   Id = dΦE/dt  

where dΦE/dt is the electric flux between the plates of capacitor

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  • According to Ampere’s circuital law, the line integral of the magnetic field around any closed path or circuit is equal to μtimes the total current

  • In the calculation of magnetic field, Ampere’s circuital law brought in several contradictions. When a different surface was used to find the magnetic field, the result was different.

  • It was concluded that a term was missing from the Ampere’s circuital law—the electric field. This electric field passes the surfaces between the plates of the capacitor used.

  • Each plate of a capacitor has an area A, and a total charge Q. Then, the magnitude of the electric field E is,

  • Using Gauss’ law, the electric flux ΦE through the surface is calculated as

  • As the charge Q on the capacitor plates changes with time, there is a current,

i = dQ/dt

This is the missing term in Ampere’s circuital law.

  • The current carried by conductors due to the flow of charges is called conduction current, and the current (new term) due to the changing electric field is called displacement current or Maxwell’s displacement current.

  • Total current, i = Conduction current (ic) + Displacement current (id)

  • Outside the capacitor plate, i = ic, and inside the capacitor plate, i = id

  • Ampere−Maxwell law is given as

The total current passing through any surface, of which the closed loop is the perimeter, is the sum of the conduction and displacement current.

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