An isolated metal sphere of radius R is electrically charged. It is connected by means of a thin connecting wire to a very distant uncharged metal sphere of radius r(r < R). Then:

The total charge is uniformly and equally distributed over the two spheres.

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The total charge is uniformly and unequally distributed over the two spheres.

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The final potential energy of the system is less than the initial potential energy.

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No amount of energy is lost in the process.

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Solution

The correct options are
B The total charge is uniformly and unequally distributed over the two spheres.
C The final potential energy of the system is less than the initial potential energy.
If there is potential difference, then charge will flow. As the radius of the two spheres are different, unequal distribution of charge takes place and there occurs loss of some energy while distributions.
Ans: $(B), (C)$

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An isolated metal sphere of radius $r$ is given a charge $q$ . The potential energy of the sphere is :

U_{1}

U_{2}

I

I I

I I

I

	Column- $I$		Column- $I I$
p.	A thin shell of radius a and having a charge – Q uniformly distributed over its surface as shown	1.	$\frac{1}{8 {πε}_{o}} \times \frac{Q^{2}}{a}$ in magnitude
q.	A thin shell of radius $\frac{5 a}{2}$ having a charge $- Q$ uniformly distributed over its surface and a point charge $- Q$ placed at its centre as shown	2.	$\frac{3}{20 {πε}_{o}} \times \frac{Q^{2}}{a}$ in magnitude
r.	A solid sphere of radius $a$ and having a charge $- Q$ uniformly distributed throughout its volume as shown	3.	$\frac{27 Q}{80 π ε_{o}} \times \frac{Q^{2}}{a}$ in magnitute
s.	A solid sphere of radius a and having a charge – Q uniformly distributed throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius $2 a$ and carrying charge $- Q$ as shown	4.	$\frac{27 Q}{60 π ε_{o}} \times \frac{Q^{2}}{a}$ in magnitude