Solving Gauss Law Question: Q/(πR^4)

[Crocodile]

Hi

Im getting a slightly different answer to the one that is needed for the following question:


2) A positive charge Q is distributed throughout a spherical volume of radius R in vacuum.
The charge density rho varies with the radius according to the linear law rho = a r. Show that the parameter a is Q/(pi R^4).


I started by saying that I'm looking at the position where r=R, i.e. at the surface itself. At this point the total charge Q must be present. Hence Q= rho x volume = a x r x volume, and as R=r Q= a x R x volume. Therefore Q = a x r x (4/3)pi R^3, which gives an a similar to the one required, but multiplied by 3/4.

Any ideas where I am going wrong?

Thanks

 

[matonski]

Q = rho x volume is only correct if rho is constant throughout the volume, which its not. This is just like distance = speed x time is only true if the speed is constant throughout the time.

 

[alibey44]

question;Two parallel, uniformly charged, infinitely long wires carry opposite charges with a linear charge density λ = 3.29 μC/m and are 5.35 cm apart. What is the magnitude of the electric field at a point midway between them and 50.3 cm above the plane containing the two wires?

my solution;http://imageshack.us/photo/my-images/189/zmsal2.jpg/

question:
The six faces of a cubical box each measure 23.0 cm by 23.0 cm, and the faces are numbered such that faces 1 and 6 are opposite to each other, as are faces 2 and 5, and faces 3 and 4. The flux through each face is:

Face Flux (N m2/C)
1 -194
2 -107
3 -251
4 -500
5 -312
6 -268
Find the net charge inside the cube.

my solution:http://imageshack.us/photo/my-images/694/zmsal3.jpg/

can you check my solutıon please,ı thınk somethıng ıs wrong about my answers...