Density, density, density. (a) A charge -318e is uniformly distributed along a c

Question

Density, density, density. (a) A charge -318e is uniformly distributed along a circular arc of radius 5.80 cm, which subtends an angle of 68° What is the linear charge density along the arc? (b) A charge -318e is uniformly distributed over one face of a circular disk of radius 4.20 cm. What is the surface charge density over that face? (c) A charge-318e is uniformly distributed over the surface of a sphere of radius 4.00 , what s the surface charge density over that surface, d) A charge 311e is rafo spread through the voume of a sphere of radius 2.80 cm. What is the volume charge density in that sphere? (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

(a) length of arc, L = (2 pi R)(theta/360)

L = (2 x pi x 0.058)(68/360)

L = 0.0688 m  

LInear charge density = Q / L

= (-318 x 1.6 x 10^-19 C) / 0.0688

= - 7.39 x 10^-16 C/m

(B) A = pi R^2 = pi (0.042^2) = 5.54 x 10^-3 m^2

surface charge density, sigma = Q / A

= - 9.18 x 10^-15 C/m^2

(C) A = 4 pi R^2 = 0.020 m^2

sigma = Q/A = - 2.53 x 10^-15 C/m^2

(d) V = 4 pi R^3 /3 = 9.195 x 10^-5 m^3

volume charge density, rho = Q/ V

= -5.53 x 10^-13 C/m^3

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