Question

A parallel plate capacitor is made of two circular plates separated by distance of 5 mm and with a dielectric with dielectric constant of 2.2 between them. When the electric field in the dielectric is 3 × 10⁴ V/cm, the charge density of the positive plate will be nearly
1. 58.5 × 10⁶ C/m²
2. 29.5 × 10⁶ C/m²
3. 29.5 × 10^-6 C/m²
4. 58.5 × 10^-6 C/m²

Answer 1

Correct Answer - Option 4 : 58.5 × 10^-6 C/m²

\(Q = CV = \frac{{{\varepsilon _0}{\varepsilon _r}A}}{d} \times V\) 

\(E = \frac{V}{d}\) 

\(\Rightarrow Q = {\varepsilon _r}{\varepsilon _0}AE\) 

\(\Rightarrow \frac{Q}{A} = {\varepsilon _r}{\varepsilon _0}E\) 

= 2.2 × 8.85 × 10^-12 × 3 × 10⁴ × 10²

= 58.41 × 10^-6 C/m²