Gauss's Law, electric field of sphere

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SUMMARY

The discussion focuses on calculating the electric field of a nonconducting sphere with a radius of 10.00 cm and a uniform volume charge density of ρ = 410 nC/m³. The total charge of the sphere is determined to be 1.717 nC. The electric field is calculated at various radii: 2.10 cm, 9.90 cm, 10.10 cm, and 13.6 cm, using the formula E = Qr / (4πR³ε₀), where ε₀ is the permittivity of free space (8.85 x 10⁻¹² F/m).

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Q:
A nonconducting sphere of radius 10.00 cm carries a uniform volume charge density ρ = 410 nC/m3.

(a) What is the total charge of the sphere?
1.717 nC

Find the electric field at the following radii.

(b) r = 2.10 cm
_____N/C

(c) r = 9.90 cm
_____kN/C

(d) r = 10.10 cm
_____N/C

(e) r = 13.6 cm
_____N/C


My attempt at the problem, after manipulating the equation EV=charge inside/[8.85x10^(-12)], was just to insert values into E=Qr/[(4*pi*R^3)*8.85x10^(-12)]; where Q is defined as the total charge, r the radius asked to calculate and R the initial radius.
 
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Your attempt is correct.
 
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