Show that the magnetic field B at a point in between the plates of a parallel plate capacitor during charging is `(mu_(0)epsilon_(0)r)/(2) (dE)/(dt)` (symbols having usual meaing). ,

Explanation

Consider the figure ginen below to prove that the magneti field B at a point in between the plater of a paravel- plate copocior during charging is `(mu_(0)epsilon_(0)r)/(2) (dE)/(dt)`

Let I_(d)be the displacement current in the region between two plates of parallel plate capacitor in the figure
The magnetic field induction at a point in a region between two plates of capacitor at a perpendcular distance r from the axis of plates is
`B=(mu_(0)2I_(d))/(4pir)=(mu_(0))/(2pir)=(mu_(0))/(2pir)xx epsilon_(0) (dphi_(E))/(dt)" "[":."I_(d)=(E_(0)dphi_(E))/(dt)]`
`=(mu_(0)epsilon_(0))/(2pir)(d)/(dt) (Epir^(2)) =(mu_(0)epsilon_(0))/(2pir)pir^(2)(dE)/(dt)`
`B=(mu_(0)epsilon_(0)r)/(2)(dE)/(dt)" "[":." phi_(E) =Epir^(2)]`