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

Let `i_c ` be the conduction current supplied to the plates of a parallel plate capacitor and ` I_d ` be the disaplacement current in the region between the two plates .Let us consider a point P in a region between the two plates of capacitor at a perpendicular distance r from the axis of the plates .
The magnetic field at point P will be
` B= ( mu _0 ) /( 4 pi ) xx ( 2 i_d )/( r) = ( mu _0 i_d )/( 2 pi r )`
` therefore i _d = epsi_0 ( d phi)/(d t ) [ phi` is the electric flux ]
`implies B= (mu _0 )/( 2 pi ) xx [ epsi_0 ( d phi )/( d t) ]`
Also ` phi = EA = E xx pi r^2 [ ` E is the electric field ]
`implies B= ( mu _0 epis_0 )/( 2 pi r ) (d)/(dt ) ( E pi r ^2) `
`=( mu_0 epsi_0 )/(2 pi r ) ( pi r^2 ) (dE )/( d t) = ( mu _0 epsi_0 r )/( 2 ) ( DE )/(dt)`