Work done enclosing sphere with spherical shell - for tommorow

[ghosts_cloak]

Hi guys!
I have been working on this question all day and am getting no where I really can't 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

 

[siddharth]

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

 

[ghosts_cloak]

Hiya,
Well, that's 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

 

[siddharth]

Hiya,
Well, that's 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

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.

 

[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!

Thanks for your help,
~Gareth

 

[siddharth]

Way to go, Gareth!