Question

A parallel plate capacitor (Fig.) made of circular plates each of radius R = 6.0 cm has a capacitance C = 100 pF. The capacitor is connected to a 230 V ac supply with a (angular) frequency of 300 rad $s^{-1}$.

(a) What is the rms value of the conduction current?

(b) Is the conduction current equal to the displacement current?

(c) Determine the amplitude of B at a point 3.0 cm from the axis between the plates.

Answer 1

$\left(a\right)$ RMS value of the conduction current, $I=\frac{V}{X_c}$

$X_c=\frac{1}{\omega C}$

$\Rightarrow I=V\omega C$

$\Rightarrow I=230\times 300\times 100\times {10}^{-12}$

$\Rightarrow I=6.9\mu A$

$\left(b\right)$ Yes. Conduction current is equal to the displacement current.

$\left(c\right)$ $B=\frac{{\mu }_{o}r{I}_o}{2\pi R^2}$

$I_o=\sqrt{2}I$

r is distance between plates from the axis,$r=0.03m$

putting values

$B=\frac{4\pi \times {10}^{-7}\times 0.03\times \sqrt{2}\times 6.9\times {10}^{-6}}{2\pi \times {0.06}^2}$

$\Rightarrow B=1.63\times {10}^{-11}T$