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this is a great forum here and i was wondering if anyone could lend a helping hand , it would be great.

im currently studying at univercity for electronics engineering and have been given some physics questions to work onover the holidays. I ahve spend quite some time on this question. and got most of the way there (i believe).

question exactly as ive been presented it:

1.Consider a sphere of radius R containing a total charge Q, in which the charge is evenly distributed throughout the sphere.

i) what is the charge density p?

ii) calculate the total charge, Q1 within a sphere of radius r, and uniform charge density p, and express this in terms of Q.

iii) calculate the total charge Q2, within a spherical shell of radius r , thichkness dr and uniform charge density p, and express this in terms of Q

Now ,show that the work done in bringing Q2 from infinity to Q1 can be written:-

dW= ((3Q^2r^4)dr)/4 pi epsilon0 R^6

well

ive worked on this question anmd so far ive come up with the following

i)p = Q/(4/3)pi.R^3

ii)Q1=(4/3)pi.r^3.p (substituting the common p for both Q1 and Q)

---> Q1=(Q.r^3)/R^3

iii)

i gather the total charge Q2 on the shell is = p.vshell

where p is common to both Q1 and Q so

Q2=p.(4/3).pi(r^3-(r-dr)^3) i got this from Q2 = charge density x (voloume of sphere radius r - volume of sphere radius (r-dr))

but i just cant work ou the last part of the answer what Dw =???

i also tried using vshell= 4pir^2dr which is surface areax shell depth

so my question is , hve i gone wrong or if not how to i get the answer to part iii in their form?

thanks

Adam Muncey

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# Electrostatics - charges on spheres and work done in moving them

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