# Work done enclosing sphere with spherical shell - for tommorow!

1. Feb 2, 2006

### ghosts_cloak

Hi guys!
I have been working on this question all day and am getting no where I really cant get to grips with Electromagnetism, arghh!
The question is :http://www.zen96175.zen.co.uk/problem.GIF
I would NOT like anyone to post a solution as its assessed work but I would IMMENSELY appreciate some pointers on how to get started on this...
I have a few hours left to complete this, I hope somebody has a few pointers :!!)
Thank you ,

~Gaz

2. Feb 2, 2006

### siddharth

So what have you done with this problem? If you show where you are stuck, it will be easier for us to help.

3. Feb 2, 2006

### ghosts_cloak

Hiya,
Well, thats the point really, I need a little push to get me started!
I am thinking it involves seeing how much work it takes to bring a hoop of charge from the spherical shell to the sphere, and then integrating over the whole shell. And then, integrate from r to a to make up the final large sphere is mentions? Pretty vague I know
Just looking for some pointers if anyone can!

Thank you!
~Gareth

4. Feb 2, 2006

### siddharth

I don't think you need to bring a hoop of charge, but you are on the right track. First find the work done in bringing the spherical shell from $\infty$ to $r$ and then integrate r from 0 to a.

To find the work done in bringing the shell, you will have to know the electric field due to sphere at the center, at a distance x and also the charge dq on the spherical shell (Hint: when the shell has finally enveloped the sphere, the charge dq is still going to be the same, so you can write dq in terms of r and dr). Then you can find the force on the spherical shell and hence the work done in bringing it to the sphere

I have not evaluated the double integral myself, but I think it should give you the answer.

Last edited: Feb 2, 2006
5. Feb 2, 2006

### ghosts_cloak

Phew, after a whole day on it, I think I have cracked it! This feeling is what makes physics and maths the greatest!!!!