(D) The potential $V$ of a conducting sphere of radius $r$ with surface charge density $\sigma$ is given by $V = \frac{\sigma r}{\varepsilon_0}$.When

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

(D) The potential $V$ of a conducting sphere of radius $r$ with surface charge density $\sigma$ is given by $V = \frac{\sigma r}{\varepsilon_0}$.When two conducting spheres are brought into contact,charge flows between them until their potentials become equal,i.e.,$V_1 = V_2$.Substituting the expression for potential,we get $\frac{\sigma_1 r_1}{\varepsilon_0} = \frac{\sigma_2 r_2}{\varepsilon_0}$.This simplifies to $\sigma_1 r_1 = \sigma_2 r_2$.Given $r_1 = R$ and $r_2 = 3R$,we have $\sigma_1 R = \sigma_2 (3R)$.Therefore,the ratio $\frac{\sigma_1}{\sigma_2} = \frac{3R}{R} = 3$.

Class 12 Physics Electric Potential and Capacitance Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

Difficult

Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated,the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$,respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

JEE MAIN 2025 All JEE MAIN

A
$\frac{1}{9}$
B
$9$
C
$\frac{1}{3}$
D
$3$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Physics Questions

Chapter

Electric Potential and Capacitance

Subtopic

Conductor, Electrostatic Shielding, Induced Charge and Charge Redistribution on conductor

Previous Year

JEE MAIN 2025 Paper All JEE MAIN years →

$A$ thin metallic spherical shell contains a charge $Q$ on it. $A$ point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in the figure. All the three charges are positive. The force on the central charge due to the shell is:

Medium

View Solution

$A$ and $B$ are two identical spheres. The charges on them are $7\,\mu C$ and $1\,\mu C$ respectively. Now,both are connected by a wire. Calculate the flow of charge from $A$ to $B$ in $\mu C$.

Medium

View Solution

The charges on two plates of a $10\,\mu F$ capacitor are $5\,\mu C$ and $15\,\mu C$. The potential difference across the capacitor plates is........$V$.

Medium

View Solution

Two charged conducting spheres $S_1$ and $S_2$ of radii $8 \text{ cm}$ and $18 \text{ cm}$ are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\frac{E_{S_1}}{E_{S_2}}$ is . . . . . . .

DifficultJEE MAIN 2026

View Solution

Two conductors of the same shape and size,one of copper and the other of aluminium (which is less conducting),are placed in a uniform electric field. What can be said about the charge induced in the aluminium conductor?

Easy

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

Two metal spheres of radius $R$ and $3R$ have the same surface charge density $\sigma$. If they are brought in contact and then separated,the surface charge density on the smaller and bigger sphere becomes $\sigma_1$ and $\sigma_2$,respectively. The ratio $\frac{\sigma_1}{\sigma_2}$ is:

Similar Questions

$A$ thin metallic spherical shell contains a charge $Q$ on it. $A$ point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in the figure. All the three charges are positive. The force on the central charge due to the shell is:

$A$ and $B$ are two identical spheres. The charges on them are $7\,\mu C$ and $1\,\mu C$ respectively. Now,both are connected by a wire. Calculate the flow of charge from $A$ to $B$ in $\mu C$.

The charges on two plates of a $10\,\mu F$ capacitor are $5\,\mu C$ and $15\,\mu C$. The potential difference across the capacitor plates is........$V$.

Two conductors of the same shape and size,one of copper and the other of aluminium (which is less conducting),are placed in a uniform electric field. What can be said about the charge induced in the aluminium conductor?

Vedclass Test Series

Exam Paper Generator

Online Exam Module