The Self Potential Energy of Continuous Charge Distributions

Q. There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to

1. 
2. 
3. 
4. 

Q.

Intuitively speaking, In which case external agent has to do more work: shell or sphere of same charge and radius?

1. Sphere
2. Equal in both.

3. Shell

4. \N

Q. A uniform charged spherical shell, 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.

A large conducting plane has a surface charge density $1.0\times {10}^{-4}C{m}^{-2.}$ Find the electrostatic energy stored in a cubical volume of edge 1.0 cm in front of the plane.

Q.

Intuitively speaking, In which case external agent has to do more work: shell or sphere of same charge and radius?

1. Shell

2. Sphere
3. Equal in both.
4. Need more data to comment.

Q. A uniform charged spherical shell, 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. $\frac{1J}{4\pi {ϵ}_0}$
   
2. $\frac{5000J}{\pi {ϵ}_0}$
   
3. $\frac{250J}{\pi {ϵ}_0}$
   
4. $\frac{2500J}{\pi {ϵ}_0}$

Q. There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to

1. $Q$
2. $Q^2$
3. $\frac{1}{R}$
4. $\frac{1}{R^2}$

Q. Find the electrostatic energy stored in a cylindrical shell of length $l$, inner radius $a$ and outer radius $b$, coaxial with a uniformly charged wire with linear charge density $\lambda$.

1. $U=\frac{{\lambda }^{2}l}{4\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$
2. $U=\frac{{\lambda }^{2}l}{8\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$
3. $U=\frac{{\lambda }^{2}l}{2\pi {\epsilon }_0}\log \left(\frac{b}{a}\right)$
4. $U=\frac{{\lambda }^{2}l}{4\pi {\epsilon }_0}\log \left(\frac{a}{b}\right)$

Q. A thick conductor having inner radius $a$ and outer radius $b$ has a small passage as shown in the figure.


A charge $+Q$ is placed at the centre. The work done by external agent in taking the charge from centre to infinity is

1. $-\frac{Q^2}{4\pi {\epsilon }_{0}a}-\frac{Q^2}{4\pi {\epsilon }_{0}b}+\frac{Q^2}{4\pi {\epsilon }_0(a-b)}$
2. $-\frac{Q^2}{8\pi {\epsilon }_{0}b}$
3. $\frac{Q^2}{8\pi {\epsilon }_{0}a}$
4. $\frac{Q^2}{8\pi {\epsilon }_{0}a}-\frac{Q^2}{8\pi {\epsilon }_{0}b}$

Q. There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to

1. $Q$
2. $Q^2$
3. $\frac{1}{R}$
4. $\frac{1}{R^2}$