Calculating Energy for Full Sphere of Radius R

[en.yokhai]

Homework Statement

hello

the question is :
what is the energy needed to build a full sphere, radii R, and with density a*r

The Attempt at a Solution

i did it this way, i assum that i have a little ball radii r, and i want to bring an intificimal sphere width dr, and use W=Kq1dq2\r

so:
q1= (a*4PIr^4)\3
dq2=a*4PIr^3

and i intigrate it from 0 to R, and my solution equals to (4a^2PIR^7)\21

and it is not as the solution says...

am i doing it right?

thanks

 

[tiny-tim]

Hi en.yokhai!

(have a pi: π and try using the X² and X₂ tags just above the Reply box )

q1= (a*4PIr^4)\3
dq2=a*4PIr^3

I don't think you can use 4/3 πr³ for q₁ …

the density varies, so you have to integrate (over spherical shells) to find the mass.

 

[berkeman]

Homework Statement

hello

the question is :
what is the energy needed to build a full sphere, radii R, and with density a*r

The Attempt at a Solution

i did it this way, i assum that i have a little ball radii r, and i want to bring an intificimal sphere width dr, and use W=Kq1dq2\r

so:
q1= (a*4PIr^4)\3
dq2=a*4PIr^3

and i intigrate it from 0 to R, and my solution equals to (4a^2PIR^7)\21

and it is not as the solution says...

am i doing it right?

thanks

Sorry for being dense guys (my density varies somewhat too...). What is the force that this work is being done against? Electric field? Gravitational field? I don't quite get it from the problem as stated so far.

 

[en.yokhai]

electric field, so the mass is not important...the charge is,namely the density