Question

An insulating, solid sphere has a uniform, positive charge density of title="\rho" alt="\rho" align="absmiddle" class="latex-formula"> =4.40*10⁻⁷C/m³. The sphere has a radius R of 0.370m.
What is the potential $V_r$ at a point located at r = 0.160 m from the center of the sphere?

Answer 1

Answer:

Vr = 7385.99 V

Explanation:

Given

ρ = 4.40*10⁻⁷C/m³

R = 0.37 m

Vr = ? when r = 0.16 m from the center of the sphere

We must get Q as follows

Q = ρ*V = ρ*(4/3)*π*R³

Q = (4.40*10⁻⁷C/m³)*(4/3)*π*(0.37 m)³

Q = 93.36*10⁻⁹C

Then we apply the equation of the potencial Vr  for r < R

Vr = (KQ/(2r))*(3 - r²/R²)

Vr = ((9*10⁹ N*m²/C²)(93.36*10⁻⁹C)/(2*0.16 m))(3 - (0.16 m)²/(0.37 m)²)

Vr = 7385.99 V