If a spherical shell has a uniform volume density of 1.84nC/m^3, inner radius a=.1m, outer radius b=.2m, what is magnitude of electric field at radial distances r=a, r=b, r=3b
Gauss Law:
at r=a, no charge is enclosed, zero E
at r=b, enclosed charge=Q=4/3 PI (b^3-a^3)*1.84nC, so figure E from kQ/b^2
E= 4kPI/3(b^3-a^3)*1.84E-9/b^2
at r=3b
E= 4kPI/27(b^3-a^3)*1.84E-9/b^2
check all that.
To find the magnitude of the electric field at different radial distances within a spherical shell, we can use the formula for electric field intensity due to a uniformly charged spherical shell. The formula is given as:
E = k * σ * r / ε₀
Where:
E is the electric field intensity
k is the Coulomb's constant (8.99 x 10^9 N m²/C²)
σ is the volume charge density
r is the radial distance from the center
ε₀ is the permittivity of free space (8.85 x 10^-12 C²/N m²)
In this case, the volume charge density (σ) is given as 1.84 nC/m³, which can be converted to C/m³ by dividing by 10^9. So, σ = 1.84 / 10^9 C/m³.
Let's calculate the electric field intensity at each of the given radial distances:
1. At r = a (inner radius):
E = k * σ * r / ε₀
= (8.99 x 10^9 N m²/C²) * (1.84 / 10^9 C/m³) * (0.1 m) / (8.85 x 10^-12 C²/N m²)
2. At r = b (outer radius):
E = k * σ * r / ε₀
= (8.99 x 10^9 N m²/C²) * (1.84 / 10^9 C/m³) * (0.2 m) / (8.85 x 10^-12 C²/N m²)
3. At r = 3b:
E = k * σ * r / ε₀
= (8.99 x 10^9 N m²/C²) * (1.84 / 10^9 C/m³) * (0.6 m) / (8.85 x 10^-12 C²/N m²)
Now, we can calculate the electric field intensity at each radial distance.