(D) For a conducting sphere of radius $R$, the capacitance $C$ in free space is given by $C = 4\pi\epsilon_0R$.The volume $V$ of the sphere is $V = (4

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

(D) For a conducting sphere of radius $R$, the capacitance $C$ in free space is given by $C = 4\pi\epsilon_0R$.The volume $V$ of the sphere is $V = (4/3)\pi R^3$.The surface area $A$ of the sphere is $A = 4\pi R^2$.Dividing the volume by the surface area, we get $V/A = [(4/3)\pi R^3] / [4\pi R^2] = R/3$.Therefore, $R = 3V/A$.Substituting this value of $R$ into the capacitance formula:$C = 4\pi\epsilon_0(3V/A) = 12\pi\epsilon_0V/A$.

Class 12 Physics Electrostatic Potential and Capacitance Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

Difficult

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is $(\epsilon_0 = \text{permittivity of free space})$

MHT CET 2026 All MHT CET

A
$2\pi\epsilon_0V/A$
B
$4\pi\epsilon_0V/A$
C
$8\pi\epsilon_0V/A$
D
$12\pi\epsilon_0V/A$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Electrostatic Potential and Capacitance

Subtopic

Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

Previous Year

MHT CET 2026 Paper All MHT CET years →

Four capacitors,each of $25\,\mu F$,are connected as shown in the figure. The $dc$ voltmeter reads $200\,V$. The charge on each plate of the capacitor is

Medium

View Solution

$A$ cylindrical capacitor has two co-axial cylinders of length $20 \, cm$ and radii $2r$ and $r$. The inner cylinder is given a charge of $10 \, \mu C$ and the outer cylinder a charge of $-10 \, \mu C$. The potential difference between the two cylinders will be:

Medium

View Solution

Consider a spherical drop of mercury of radius $R$ with capacitance $C = 4 \pi \epsilon_0 R$. If two such droplets combine to form a larger one,what would be its capacitance in terms of $C$?

MediumTS EAMCET 2021

View Solution

Between a solid sphere and a hollow sphere of the same radius, which has a greater capacity to hold electric charge?

Easy

View Solution

Two similar conducting balls having charges $+q$ and $-q$ are placed at a separation $d$ from each other in air. The radius of each ball is $r$ and the separation between their centres is $d$ $(d \gg r)$. Calculate the capacitance of the two-ball system.

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is $(\epsilon_0 = \text{permittivity of free space})$

Similar Questions

Four capacitors,each of $25\,\mu F$,are connected as shown in the figure. The $dc$ voltmeter reads $200\,V$. The charge on each plate of the capacitor is

$A$ cylindrical capacitor has two co-axial cylinders of length $20 \, cm$ and radii $2r$ and $r$. The inner cylinder is given a charge of $10 \, \mu C$ and the outer cylinder a charge of $-10 \, \mu C$. The potential difference between the two cylinders will be:

Consider a spherical drop of mercury of radius $R$ with capacitance $C = 4 \pi \epsilon_0 R$. If two such droplets combine to form a larger one,what would be its capacitance in terms of $C$?

Between a solid sphere and a hollow sphere of the same radius, which has a greater capacity to hold electric charge?

Two similar conducting balls having charges $+q$ and $-q$ are placed at a separation $d$ from each other in air. The radius of each ball is $r$ and the separation between their centres is $d$ $(d \gg r)$. Calculate the capacitance of the two-ball system.

Vedclass Test Series

Exam Paper Generator

Online Exam Module