Calculate the total charge on a sphere

[nosmas]

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

 

[SammyS]

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 = 4πr²(ρ₀/R)r dr .

4, π, ρ₀, and R are all constants.

Integrate that over the entire sphere. → r goes from 0 to R .

 

[nosmas]

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?

 

[SammyS]

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 .