Calculate the total charge on a sphere

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Homework Statement


Using integration calculate the total charge on the sphere

radius R
Volume charge density at the surface of the sphere p0

p = p0r/R



I started with dq = 4*pi*r^2*dr*(p0r/R)

but i am not sure how to integrate (in terms of what variable I would assume r=0 to r=R) but i am not sure i set up the question right
 
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  • #2
SammyS
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Homework Statement


Using integration calculate the total charge on the sphere

radius R
Volume charge density at the surface of the sphere p0

p = p0r/R

I started with dq = 4*pi*r^2*dr*(p0r/R)

but i am not sure how to integrate (in terms of what variable I would assume r=0 to r=R) but i am not sure i set up the question right
I presume that you mean ρ = ρ0(r/R) is the volume charge density for a sphere of radius, R, where ρ0 is the volume charge density at the surface of the sphere.

The volume element is dV = 4πr2dr.

So that dq = 4πr2(ρ)dr = 4πr20/R)r dr .

4, π, ρ0, and R are all constants.

Integrate that over the entire sphere. → r goes from 0 to R .
 
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That makes sense so if I was asked to find the E field using gauss's law for r<=R would I just use E=q/(area*epsilon) but how would I know what q enclosed is???
 
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SammyS
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That makes sense so if I was asked to find the E field using gauss's law for r<=R would I just use E=q/(area*epsilon) but how would I know what q enclosed is???
To find the charge enclosed in a sphere of radius, r, integrate from 0 to r .
 

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