Show that the magnetic field B at a poin...

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). ,

Text Solution

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Let `I_D` be the displacement current in the region between two plates
of parallel plate capacitor, Fig. The magnetic field
induction at a point in a region between two plates of capacitor at
`abotr` distance r from the axis of plate is
`B=(mu_0)/(4pi) (2I_D)/r=(mu_0)/(2pir) I_D=(mu_0)/(2pir)xxin_0 (d phi_E)/(dt) [ :' I_D=in_0 (dphi_E)/(dt)]`
`=(mu_0in_0)/(2pir) d/(dt) (Epir^2)=(mu_0in_0)/(2pir) pir^2 (dE)/(dt) =(mu_0in_0 r)/2 (dE)/(dt) ( :' phi_E=Epir^2)`

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Dimension of (1)/(mu_(0)epsilon_(0)) , where symbols have usual meaning, are

(a) `[L^(-1)T]`

(b) `[L^(-2)T^(2)]`

( c ) `[L^(2)T^(-2)]`

(d) `[LT^(-1)]`

The magnetic field between the plates of a capacitor when r gt R is given by-

`(mu_(0)I_(D)r)/(2piR^(2))`

`(mu_(0)I_(D))/(2piR )`

`(mu_(0)I_(D))/(2pir)`

zero

The electrostatic force between the metal plates is isolated parallel plate capacitor C having a charge area A, is

Proportional to the square root of the distance the plates.

Linearly proportional to the distance between the

Indepdent of the distance between the plates

Inversely proportional to the distance between the plates