Read the following passage and then answer questions (a) to (d) on the basis of your under- standing of the passage and the related studied concepts.
We are familiar with Ampere.s circuital law which states that for an open surface with a boundary around a current the line integral of magnetic field around the entire boundary of an open surface is equal to `mu_(0)` times the total current passing through the surface i.e.
`ointvecB.vec(dl)=mu_(0)I`
Later on, Maxwell showed that for logical consistency, a changing electric field must also produce a magnetic field. In this context Maxwell introduced the concept of a displacement current given as per relation
`I_(D)=in_(0)(dphi_(E))/(dt)`
Thus, as per generalisation made by Maxwell, the source of a magnetic field is not just the conduction electric current due to following charges but also the time rate of change of electric field. In this way, Maxwell modified Ampere.s circuital law and in its modified the law is expressed as:
`ointvecB.vec(dl)=mu_(0)[I_(C )+I_(D)]=mu_(0)[I_(C )+in_(0)(dphi_(E))/(dt)]`
In all respects, the displacement current has the same physical effects as the conduction current. It is observed that in same cases, e.g., steady electric field in a wire, displacement current may be zero. In other cases, e.g., a capacitor being charged, both conduction and displacement currents may be present in different regions of space. In most of the cases, conduction current and displacement current may be present simultaneously in the same region of space because there exist no perfectly conducting or perfectly insulating medium. Moreover, there may be large regions of space where there is no conduction current but there is only a displacement current due to time varying electric field.
Define displacement current.

Explanation

(a) Displacement current is the current set up in space due to a time varying electric field.
Mathemtically,
`I_(D)=in_(D)=(dphi_(E))/(dt)`
where `(dphi_(E))/(dt)=`time rate of change of electric flux of a given region in space.