
Two isolated conducting spheres ${S_1}$ and ${S_2}$ of radius $\dfrac{2}{3}R$ and $\dfrac{1}{3}R$ have $12\mu C$ and $ - 3\mu C$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on ${S_1}$ and ${S_2}$are respectively:
(A) $6\mu C$ and $3\mu C$
(B) $4.5\mu C$ on both
(C) $4.5\mu C$ and $ - 4.5\mu C$
(D) $3\mu C$ and $6\mu C$
Answer
163.8k+ views
Hint: In order to solve this question, we will use the concept that the sum of charges will remain the same before and after joining both spheres, and after joining the sphere through the wire, both spheres will have the same potential and hence by forming two equations we will solve for a charge on each sphere.
Formula used:
Potential on a sphere in terms of charge and radius is given by:
$V = \dfrac{{KQ}}{R}$
Where Q is charge, R is radius and K is constant.
Complete answer:
Let us draw the rough diagram of before and after joining the spheres as

So, the sum of charges will remain same after joining the sphere as
$
{q_1} + {q_2} = 12 - 3 \\
{q_1} + {q_2} = 9\mu C \to (i) \\
$
Now, after joining the spheres, the potential remains the same, and using the formula $V = \dfrac{{KQ}}{R}$ for both sphere we get,
$
\dfrac{{K{q_1}}}{{(\dfrac{2}{3}R)}} = \dfrac{{K{q_2}}}{{(\dfrac{1}{3})R}} \\
{q_1} = 2{q_2} \to (ii) \\
$
Now, solving equations (i) and (ii) we get,
$
3{q_2} = 9 \\
{q_2} = 3\mu C \\
$
and
$
{q_1} = 9 - 3 \\
\Rightarrow {q_1} = 6\mu C \\
$
So, the charges on spheres ${S_1}$ and ${S_2}$ are $6\mu C$ and $3\mu C$.
Hence, the correct answer is option (A) $6\mu C$ and $3\mu C$
Note: It should be remembered that whenever the two charge spheres are joined together by a wire they share a common potential but the charges are distributed among them according to their radius and thus depend upon the capacitance of the spheres. and $\mu C$ is the smaller unit of charge and it’s related as $1\mu C = {10^{ - 6}}C$.
Formula used:
Potential on a sphere in terms of charge and radius is given by:
$V = \dfrac{{KQ}}{R}$
Where Q is charge, R is radius and K is constant.
Complete answer:
Let us draw the rough diagram of before and after joining the spheres as

So, the sum of charges will remain same after joining the sphere as
$
{q_1} + {q_2} = 12 - 3 \\
{q_1} + {q_2} = 9\mu C \to (i) \\
$
Now, after joining the spheres, the potential remains the same, and using the formula $V = \dfrac{{KQ}}{R}$ for both sphere we get,
$
\dfrac{{K{q_1}}}{{(\dfrac{2}{3}R)}} = \dfrac{{K{q_2}}}{{(\dfrac{1}{3})R}} \\
{q_1} = 2{q_2} \to (ii) \\
$
Now, solving equations (i) and (ii) we get,
$
3{q_2} = 9 \\
{q_2} = 3\mu C \\
$
and
$
{q_1} = 9 - 3 \\
\Rightarrow {q_1} = 6\mu C \\
$
So, the charges on spheres ${S_1}$ and ${S_2}$ are $6\mu C$ and $3\mu C$.
Hence, the correct answer is option (A) $6\mu C$ and $3\mu C$
Note: It should be remembered that whenever the two charge spheres are joined together by a wire they share a common potential but the charges are distributed among them according to their radius and thus depend upon the capacitance of the spheres. and $\mu C$ is the smaller unit of charge and it’s related as $1\mu C = {10^{ - 6}}C$.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Charging and Discharging of Capacitor

Instantaneous Velocity - Formula based Examples for JEE

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

In which of the following forms the energy is stored class 12 physics JEE_Main

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Other Pages
Three mediums of refractive indices mu 1mu 0 and mu class 12 physics JEE_Main

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks

NEET Marks vs Rank 2024|How to Calculate?
