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:

  ---1.

But between the plates there exists no conduction current, thus the contour C1 encloses no current thus.

  ---2.

Again, applying Ampere circuital law in contour C2 gives

   ---3.

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

 ---4.

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.

Mathematically,