Electric field at points A, B, and C inside a hollow ball?

AI Thread Summary
The discussion revolves around calculating the electric field at points A, B, and C inside a hollow ball situated within a larger charged ball. The approach involves determining the electric field contributions from both the original solid ball and an imaginary hollow ball with a negative charge density. It is established that the electric field at point C, located at the center of the larger ball, is zero. The calculations for points A and B require considering the respective distances from the center of the larger ball and applying Gauss's law accordingly. The final electric field values need to be clarified for each point based on the derived equations and the specific geometry involved.
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as seen in the diagram below, ->
http://picasaweb.google.com/devanlevin/DropBox?authkey=Gv1sRgCL_4l4PpvP_YsQE#5314956645280048530

is a solid ball with a radius of R=5cm and a charge density of \rho=-3\muC/m3,
inside this ball, we make a hollow ball shaped space with a radius of R/3 with its centre at 2R/3 from the centre of the big ball.

what is the Electric field at point:

A-on the leftmost point of the hollow
B-on the top point of the hollow
C-at the centre of the big ball

---------------------------------------------------
how do i do this?

i think what i need to do is say that the field is equal to (the field of the original ball) + ( the field of a ball the size of the hollow, with a charge density of -\rho )??

for C i know that the field before is 0 since it is at the centre, how do i continue from there?
 
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what i did so far is: E=epsilon0
i took a surface at the radius of the ball and said

\varphi=\ointEdA=EA=E(4\piR2)

\varphi=Q/E=(V\rho)/E=(0.75\piR3/E)

E(4\piR2)=(0.75\piR3/E)
E=(\rhoR)/(3E)

now what i will do is subtract the "field" of the imaginary ball from the field of the big ball to get the total

E=E1-E2
E=(\rhoR)/(3E)-(\rhoR)/(9E)
and i get

E=(2\rhoR)/(9E)
but where is this answer valid for? A,B or C?? is this the field at A since i took the radius of the big ball and found the flux according to that? for the others do i need to do the same using the radius 2R/3 for point B and C and saying the field of the big ball alone at C is 0?
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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