A sphere of radius 5.00 cm carries charge 3.00 nC. Calculate the electric-field magnitude at a distance 4.00 cm from the center

Question

Citrus2011

9 days ago

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A sphere of radius 5.00 cm carries charge 3.00 nC. Calculate the electric-field magnitude at a distance 4.00 cm from the center

of the sphere and at a distance 6.00 cm from the center of the sphere if the sphere is a solid insulator with the charge spread uniformly throughout its volume. Express your answers in newtons per coulomb separated by a comma. Repeat part A if the sphere is a solid conductor.

Physics

1 answer:

ValentinkaMS [1.1K] · Answer 1 · 2026-02-24T02:08:03+03:00

Answer:

a) E = 8.63 10³ N /C, E = 7.49 10³ N/C

b) E= 0 N/C, E = 7.49 10³ N/C

Explanation:

a) We can apply Gauss's law for this problem,

Ф = ∫ E. dA = $q_{int}$ /ε₀

By taking a spherical Gaussian surface, the electric field lines are parallel to the sphere's radius, simplifying the scalar product to an algebraic one.

The surface area of a sphere is given by:

A = 4π r²

Using the density formula:

ρ = q_{int} / V

q_{int} = ρ V

The sphere's volume is calculated as:

V = 4/3 π r³

Substituting in, we get:

E 4π r² = ρ (4/3 π r³) /ε₀

E = ρ r / 3ε₀

The density then is:

ρ = Q / V