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The figure shows a capacitor made of two...

The figure shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm . The capacitor is beging charged by an external source (not shown in the figure. ) The charing is constant and equal to 0.15 A

Obtain the displacement current across the plates.

Text Solution

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(a) `C=epsi_(0)A//d =80.1 pF`
`(dQ)/(dt) =C ""(dV)/(dt)`
`(dV)/(dt) =(0.15)/(80.1xx10^(-12))=1.87xx10^(9) V s^(-1)`
(b) `i_(d) =epsi_(0) ""(d)/(dt) Phi _(E)`. Now across the capacitor `Phi_(E)=EA`, ignoring and corrections.
Therefore, `i_(d)=epsi_(0)A""(d Phi_(E))/(dt)`
Now, `E=(Q)/(epsi_(0)A)`. Therefore, `(dE)/(dt)=(i)/(epsi_(0) A)`, which implies `i_(d)=i=0.15 A.`
(c) Yes, provided by ‘current’ we mean the sum of conduction and displacement currents.
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