Find the distance d (in mm) between the plate | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The capacitance of a parallel plate capacitor is given by $C_p = \frac{\epsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plates and $r$ is

Vedclass · Accepted Answer

$0.1$

Vedclass · Answer

(B) The capacitance of a parallel plate capacitor is given by $C_p = \frac{\epsilon_0 A}{d}$,where $A = \pi r^2$ is the area of the plates and $r$ is the radius of the plates.Given diameter $= 40\, mm$,so radius $r = 20\, mm = 20 	imes 10^{-3}\, m$.The capacitance of an isolated metallic sphere is given by $C_s = 4\pi \epsilon_0 R$,where $R = 1\, mm = 1 	imes 10^{-3}\, m$.Equating the two capacitances: $\frac{\epsilon_0 A}{d} = 4\pi \epsilon_0 R$.Substituting $A = \pi r^2$: $\frac{\pi r^2}{d} = 4\pi R$.Solving for $d$: $d = \frac{r^2}{4R}$.Substituting the values: $d = \frac{(20 	imes 10^{-3})^2}{4 	imes 1 	imes 10^{-3}} = \frac{400 	imes 10^{-6}}{4 	imes 10^{-3}} = 100 	imes 10^{-3}\, m = 0.1\, mm$.

Find the distance $d$ (in $mm$) between the plates of a parallel plate capacitor with a plate diameter of $40\, mm$,such that its capacitance is equal to the capacitance of a metallic sphere of radius $1\, mm$.

Similar Questions

The potential difference between two plates of a parallel plate capacitor is $2V$. As shown in the figure, electrons are placed at point $P$ and $Q$. So,

The electrostatic force between the metal plates of an isolated parallel plate capacitor $C$ having a charge $Q$ and area $A$ is

Three plates $A, B$ and $C$ each of area $0.1 \ m^2$ are separated by $0.885 \ mm$ from each other as shown in the figure. A $10 \ V$ battery is used to charge the system. The energy stored in the system is

In a parallel plate capacitor,if $10^{12}$ electrons pass from one plate to another,a potential difference of $10 \,V$ is developed across the plates. The capacitance of the capacitor is

Vedclass Test Series

Exam Paper Generator

Online Exam Module