Answer

Verified

421.5k+ views

**Hint:**After the spheres are joined, basically the potential of the spheres will become the same but the total charge would be the same as before. So, we get two equations- one from the total charge and the other from the equal potential – on solving which we can get the amount of charge flow.

**Complete step by step answer:**

Consider the two spheres ${S_1}$ and ${S_2}$ with radii ${R_1},{R_2}$ and charges ${Q_1},{Q_2}$ respectively.

According to the question, we are given

$

{R_1} = R \\

\Rightarrow{R_2} = 2R \\

\Rightarrow{Q_1} = q \\

\Rightarrow{Q_2} = - 2q \\

$

So, the total initial charge can be given by,

$

{Q_{ini}} = {Q_1} + {Q_2} = q + \left( { - 2q} \right) \\

\Rightarrow{Q_{ini}} = - q \\

$

Now, on joining the two spheres the charge starts flowing from one sphere to another until both the spheres reach the same potential, but the total charge remains the same.

Let ${Q_1}^\prime ,{Q_2}^\prime $ be the new charges on spheres respectively and let their potentials be ${V_1},{V_2}$ after being joined. So, according to the conditions,

$

{Q_1}^\prime + {Q_2}^\prime = {Q_{ini}} \\

\Rightarrow {Q_1}^\prime + {Q_2}^\prime = - q \\

$

Also, the potentials of both the spheres will be equal,

\[

{V_1} = {V_2} \\

\Rightarrow \dfrac{{k{Q_1}^\prime }}{{{R_1}}} = \dfrac{{k{Q_2}^\prime }}{{{R_2}}} \\

\Rightarrow \dfrac{{{Q_1}^\prime }}{R} = \dfrac{{{Q_2}^\prime }}{{2R}} \\

\Rightarrow {Q_1}^\prime = \dfrac{{{Q_2}^\prime }}{2} \\

\]

On solving the above two equations we get,

\[{Q_2}^\prime = \dfrac{{ - 2q}}{3}\] and ${Q_1}^\prime = \dfrac{{ - q}}{3}$

Now, we can find the charge flow by subtracting the final charge from the initial charge on any of the spheres as

$\therefore{Q_{flow}} = q - \left( { - \dfrac{{2q}}{3}} \right) = \dfrac{{4q}}{3}$

**Therefore, the correct option is D.**

**Note:**We can find the charge flow from any of the spheres because the flow would be the same for both the spheres. Also, the main points to be noted here are that the total charge remains the same and the flow of charge only occurs till both the spheres reach the same potential.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Onam is the main festival of which state A Karnataka class 7 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Who was the founder of muslim league A Mohmmad ali class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers