The Self Potential Energy of a Solid Sphere

Q. A uniformly charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

1. 
   
2. 
3. 
   
4. 
   

Q. In the given figure, sphere $1$ is a conducting sphere while sphere $2$ is a non-conducting solid sphere of radius $a$ and $b$ respectively. The distance between centres is $d$. Find the total energy of the arrangement. $(d>>a,d>>b)$

1. $\frac{Q_1^2}{8\pi {\epsilon }_{0}a}+\frac{3Q_2^2}{20\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{4\pi {\epsilon }_{0}d}$
2. $\frac{Q_2^2}{8\pi {\epsilon }_{0}a}+\frac{3Q_1^2}{8\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{8\pi {\epsilon }_{0}d}$
3. $\frac{Q_2^2}{4\pi {\epsilon }_{0}a}+\frac{3Q_1^2}{8\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{8\pi {\epsilon }_{0}d}$
4. None of above

Q. A uniform charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

1. 
   
2. 
   
3. 
   
4. 

Q. In the given figure, sphere $1$ is a conducting sphere while sphere $2$ is a non-conducting solid sphere of radius $a$ and $b$ respectively. The distance between centres is $d$. Find the total energy of the arrangement. $(d>>a,d>>b)$

1. $\frac{Q_1^2}{8\pi {\epsilon }_{0}a}+\frac{3Q_2^2}{20\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{4\pi {\epsilon }_{0}d}$
2. $\frac{Q_2^2}{8\pi {\epsilon }_{0}a}+\frac{3Q_1^2}{8\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{8\pi {\epsilon }_{0}d}$
3. $\frac{Q_2^2}{4\pi {\epsilon }_{0}a}+\frac{3Q_1^2}{8\pi {\epsilon }_{0}b}-\frac{Q_1{Q}_2}{8\pi {\epsilon }_{0}d}$
4. None of above

Q. STATEMENT-1
For practical purposes, the earth is used as a reference at zero potential in electrical circuits.
and
STATEMENT-2
The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by $\frac{Q}{4\pi {ϵ}_{0}R}$.

1. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
2. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
3. STATEMENT -1 is True, STATEMENT-2 is False
4. STATEMENT -1 is False, STATEMENT-2 is True

Q. A uniformly charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

1. $\frac{6000J}{\pi {ϵ}_0}$
2. $\frac{5000J}{\pi {ϵ}_0}$
3. $\frac{24000J}{\pi {ϵ}_0}$
4. $\frac{25000J}{\pi {ϵ}_0}$

Q. A capacitor of capacitance $C$ is charged to a potential difference $V.$ The flux of the electric field through a closed surface enclosing the capacitor is

1. $\frac{CV}{{\epsilon }_0}$
2. $\frac{2CV}{{\epsilon }_0}$
3. $\frac{CV}{2{\epsilon }_0}$
4. zero

Q. A uniformly charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

1. $\frac{6000J}{\pi {ϵ}_0}$
2. $\frac{5000J}{\pi {ϵ}_0}$
3. $\frac{24000J}{\pi {ϵ}_0}$
4. $\frac{25000J}{\pi {ϵ}_0}$

Q. A uniformly charged sphere, entirely made up of charges in vacuum, has a total charge 20 C and radius 10 mm. With reference to infinity, what is the self-potential energy of the system?

1. $\frac{6000J}{\pi {ϵ}_0}$
2. $\frac{5000J}{\pi {ϵ}_0}$
3. $\frac{24000J}{\pi {ϵ}_0}$
4. $\frac{25000J}{\pi {ϵ}_0}$

Q. Two metallic spheres $A$ and $B$ are made of the same material and have got an identical surface finish. The mass of sphere $A$ is four times that of $B$. Both the spheres are heated to the same temperature and placed in a room having lower temperature but thermally insulated from each other.

1. The ratio of rate of heat loss of $A$ to that of $B$ is $2^{4/3}$.
2. The ratio of heat loss of $A$ to that of $B$ is $2^{2/3}$.
3. The ratio of the initial rate of cooling of $A$ to that of $B$ is $2^{-2/3}$
4. The ratio of the initial rate of cooling of $A$ to that of $B$ is $2^{-4/3}$