- #1

gnrlies00

- 20

- 0

## Homework Statement

Consider a non-conducting sphere of radius 'R' and charge 'Q' is enclosed by spherical shell of radius '5R' and charge '4Q'. If inner sphere is expanded to radius '3R'.Then amount of work done by the field in this process is

## Homework Equations

W=ε

_{0}/2∫E

^{2}dτ

## The Attempt at a Solution

first find the energy of the non-conducting sphere of radius R and charge Q

W=ε

_{0}/2k

^{2}Q

^{2}(∫

_{R}

^{∞}1/r

^{4}(r

^{2}4π)dr + ∫

_{0}

^{R}(r/R

^{3})

^{2}(4πr

^{2})dr)

⇒ W=3kQ

^{2}/ 5R ---------------------------(1)

Similarly, find W for spherical shell

⇒ W=8kQ

^{2}/ 5R -------------------------(2)

Subtracting (2) from (1)

W= kQ

^{2}/5R = kQ

^{2}/R ----------------(3)

For the remaining part I'm confused...

Should I find the work done for the new expanded sphere(i.e. Radius = 3R) and subtract it from equation(3)..

If yes, then what limits should I take for the integral ∞ to 3R (for outside E) and 3R to 0 (for inside E)?

Am I going about the problem correctly or missing something?

Please help.