The Self Potential Energy of Continuous Charge Distributions

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

Q.

Figure shows two identical spheres A and B carrying +4 V and -4V potential respectively.

Which sphere has more potential?

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.