what is displacement current????
what is conduction current???
Conduction current is the electric current that flows through a conductor because of an applied potential difference.
Displacement current appears as a theoretical necessity in situations where non steady current is encountered. Suppose let us consider a charging capacitor (not has been completely charged yet) consisting of parallel plates as shown in the figure. Now it has been found that if we keep a magnetic needle between the plates it will shows a deflection indicating that there exists a magnetic field between plates.
Now according to Ampere circuital law there must exists a current flow to have a magnetic field according to the relation:
But between the plates there exists no conduction current, thus the contour C1 encloses no current thus.
Again, applying Ampere circuital law in contour C2 gives
But eqn. 1 and eqn. 2 gives a contradiction.
Thus to resolve the contradiction Maxwell proposed that Ampere circuital should be modified and an invisible current is to be considered that gives rise to a magnetic field between the capacitor plates. Thus, Ampere-Maxwell law became
Maxwell argued that the electric field is changed between the plates due to mounting charge on the plates and a changing electric field gives rise to a magnetic field.
Thus displacement current is the current that is included to explain the magnetic field inside the capacitor due to mounting up of charges on its plates.
In simple lang. - conduction current is the result of current due to charges at rest.displacement current is due to motion of charge carriers
The conduction current is
You know how V varies with respect to t. You will need to find C, which is not that difficult.
The displacement current D can be calculated from