Question

Density, density, density. (a) A charge -344e is uniformly distributed along a circular arc of radius 4.80 cm, which subtends an angle of 59°. What is the linear charge density along the arc? (b) A charge -344e is uniformly distributed over one face of a circular disk of radius 4.50 cm. What is the surface charge density over that face? (c) A charge -344e is uniformly distributed over the surface of a sphere of radius 3.10 cm. What is the surface charge density over that surface? (d) A charge -344e is uniformly spread through the volume of a sphere of radius 3.20 cm. What is the volume charge density in that sphere? (a) Number T9.211e-15 (b) Numbe (c) Number (d) Number Click if you would like to Show Work for this question: UnitsT C/m Units Uni Units Open Show Work

Answer 1

Given,

q = -344 e ; r = 4.8 cm ; theta = 59

q = -344 x 1.6 x 10^-19 = -5.5 x 10^-17 C

lambda = q/L

L = r theta(radians)

L = 4.8 x 1.03 = 4.94 cm

lambda = -5.5 x 10^-17/0.0494 m = -1.11 x 10^-15

Hence, lambda = -1.11 x 10^-15 C/m

b)r = 4.5 cm

sigma = Q/A = Q/pi r^2

sigma = -5.5 x 10^-17/(3.14 x 0.045^2) = -8.65 x 10^-15 C/m^2

Hence, sigma = -8.65 x 10^-15 C/m^2

c)r = 3.1 cm

sigma = Q/V = Q/4 pi r^2

sigma = -5.5 x 10^-17/(4 x 3.14 x 0.031^2) = -4.56 x 10^-15 C/m^2

Hence, sigma = -4.56 x 10^-15 C/m^2

d)r = 3.2 cm

rho = Q/V = Q/(4/3 pi r^3)

rho = -5.5 x 10^-17/(4/3 x 3.14 x 0.02^3) = -1.64 x 10^-12 C/m^3

Hence, rho = -1.64 x 10^-12 C/m^3