Density, density, density. (a) A charge -360e is uniformly distributed along a c

Question

Density, density, density. (a) A charge -360e is uniformly distributed along a circular arc of radius 6.00 cm, which subtends an angle of 66o. What is the linear charge density along the arc? (b) A charge -360e is uniformly distributed over one face of a circular disk of radius 4.00 cm. What is the surface charge density over that face? (c) A charge -360e is uniformly distributed over the surface of a sphere of radius 5.00 cm. What is the surface charge density over that surface? (d) A charge -360e is uniformly spread through the volume of a sphere of radius 3.40 cm. What is the volume charge density in that sphere?

Explanation / Answer

(A) length = theta * r = (66 pi / 180) (0.06 m)

L = 0.069 m

linear charge density = (-360 x 1.6 x 10^-19) / 0.069

= - 8.33 x 10^-16 C/m

(B) A = pi r^2 =pi x 0.04^2 = 5.0265 x 10^-3 m^2

surface charge density = (-360 x 1.6 x 10^-19) / A

= 1.15 x 10^-14 C/m^2

(C) A = 4 pi R^2 = 0.0314 m^2

surface charge density = Q / A = 1.83 x 10^-15 C/m^2

(D) V = 4 pi R^3 /3 = 1.646 x 10^-4 m^3

Volume charge density = Q / V

= 3.50 x 10^-13 C / m^3

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