Respuesta :
Answer:
[tex]1.57 * 10^{3} Q[/tex]
Explanation:
The volume charge density is defined by ρ = [tex]\frac{Q}{V}[/tex] (Equation A), where Q is the charge and V, the volume.
The units in the S.I. are [tex]\frac{Coulombs}{m^{3} }[/tex], so we have to express the radius in meters:
inner radius = [tex]4 cm * \frac{1 m}{100 cm} = 0.04m[/tex]
outer radius = [tex]6 cm * \frac{1m}{100cm} = 0.06m[/tex]
Now, we know that the volume of the sphere is calculated by the formula:
[tex]V = \frac{4}{3}\pi r^{3}[/tex], and as we have an spherical shell, the volume is calculated by the difference between the outher and inner spheres:
V = [tex]\frac{4}{3}\pi (r_{o} ^{3} - r_{i} ^{3})[/tex], where [tex]r_{o}[/tex] is the outer radius and [tex]r_{i}[/tex] is the inner radius.
Replacing the volume formula in the Equation A:
ρ = [tex]\frac{Q}{\frac{4}{3}\pi(r^{3} _{o}-r_{i} ^{3})}[/tex]
ρ = [tex]\frac{3Q}{4\pi (r_{o} ^{3}-r_{i} ^{3} ) }[/tex]
Replacing the values of the outer and inner radius whe have:
ρ = [tex]\frac{3Q}{4\pi (1.52 * 10^{-4})}[/tex]
ρ = [tex]1.57 * 10^{3} Q[/tex]
