Find charge density rho of a uniform shpere with radius R

In summary, the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q can be found by using the equations ρ= qtot/(4/3)piR^3 and dq= ρ*Venc. The charge density is given by ρ= qtot/((4/3)piR^3) and the integral ∫dq = ∫q*(r^3/R^3)dr⇒ q*(¼r^4/R^3) does not seem to be the correct approach.
  • #1
Andrew11
2
0

Homework Statement


Find the potential V(r) inside and outside of a uniformly charged sphere with radius R and total charge q.
A) Fix first the charge density ρ(r) in the two regions 1: r>R and 2: 0<r<R the results should only be in terms of q and R[/B]

Homework Equations


ρ= qtot/Vtot
dq= ρ*Venc

The Attempt at a Solution


ρ= qtot/(4/3)piR^3
dq = [(qtot/(4/3)piR^3)*(4/3)pir^3]dr⇒(q*r^3/R^3)
∫dq = ∫q*(r^3/R^3)dr⇒ q*(¼r^4/R^3)

not sure if this is the correct approach to the problem
 
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  • #2
ρ= qtot/(4/3)piR^3
Don't forget brackets: ρ= qtot/((4/3)piR^3) or ##\rho = \frac{3q}{4\pi R^3}##. Also, is this the charge density everywhere?
I don't understand what you are trying to do in the two lines below. You found the charge density, what does the integral mean and why do you integrate over a charge?
 

1. How is the charge density of a uniform sphere with radius R calculated?

The charge density of a uniform sphere with radius R is calculated by dividing the total charge of the sphere by its volume. This can be expressed by the formula ρ = Q/V, where ρ is the charge density, Q is the total charge, and V is the volume of the sphere.

2. What is the formula for calculating the volume of a sphere?

The formula for calculating the volume of a sphere is V = (4/3)πR³, where V is the volume, π is the constant pi, and R is the radius of the sphere.

3. Can the charge density of a uniform sphere with radius R be negative?

No, the charge density of a uniform sphere with radius R cannot be negative. Charge density is a measure of the amount of charge per unit volume, and since charge is a positive quantity, the charge density will always be positive.

4. How does the charge density of a uniform sphere with radius R change as the radius increases?

The charge density of a uniform sphere with radius R will decrease as the radius increases. This is due to the fact that the volume of the sphere increases at a faster rate than the total charge, resulting in a lower charge density.

5. Is the charge density of a uniform sphere with radius R the same at all points within the sphere?

Yes, the charge density of a uniform sphere with radius R is the same at all points within the sphere. This is because the charge is evenly distributed throughout the sphere, resulting in a uniform charge density.

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