Figure 8.6 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.
(a) Calculate the capacitance and the rate of change of potential difference between the plates.
(b) Obtain the displacement current across the plates.
(c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

Explanation

(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.