Density, density, density, (a) A charge -356e is uniformly distributed along a c

Question

Density, density, density, (a) A charge -356e is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 59 degree. What is the linear charge density along the are? (b) A charge -356e is uniformly distributed over one face of a circular disk of radius 5.00 cm. What is the surface charge density over that face? (c) A charge -356e is uniformly distributed over the surface of a sphere of radius 2.30 cm. What is the surface charge density over that surface? (d) A charge -356e is uniformly spread through the volume of a sphere of radius 3.70 cm. What is the volume charge density in that sphere? (a) Number Units b) Number Units c) Number Units d) Number Units

Explanation / Answer

(A) length = theta r

theta = 59 deg = 59 x pi / 180 rad

L = (59 x pi / 180) (4) = 4.12 cm = 0.0412 m

charge density = Q / L = (-356 x 1.6 x 10^-18) / 0.0412

= - 1.385 x 10^-15 C/ m

(b) A = pi (5^2) = 78.54 cm^2 = 78.54 x 10^-4 m^2

Q = - 356 x 1.602 x 10^-19 C

charge density = Q / A = - 7.26 x 10^-15 C / m^2

(c) A = 4 pi r^2 = 66.48 cm ^2 = 66.48 x 10^-4 m^2

charge density = Q / A = -8 .57 x 10^-15 C / m^2

(D) V = 4 pi R^3 / 3 = 212.17 cm^3 = 212.17 x 10^-6 m^3

volume charge density = Q / V = 2.685 x 10^-13 C / m^3

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