Density, density, density. (a) A charge -306e is uniformly distributed along a c

Question

Density, density, density. (a) A charge -306e is uniformly distributed along a circular arc of radius 5.80 cm, which subtends an angle of 55o. What is the linear charge density along the arc? (b) A charge -306e is uniformly distributed over one face of a circular disk of radius 2.80 cm. What is the surface charge density over that face? (c) A charge -306e is uniformly distributed over the surface of a sphere of radius 2.10 cm. What is the surface charge density over that surface? (d) A charge -306e is uniformly spread through the volume of a sphere of radius 4.00 cm. What is the volume charge density in that sphere?

Explanation / Answer

(a) the charge will be divided by the length a complete circle would be 2Pi*r, we only have 55/360 of a complete circle. so we have -306e/{(2Pi5.80cm)(55/360)} = -306e/5.57cm = -55.0e/cm (b) the charge will be divided by the area. the area is Pi r^2 -306e/{Pi(2.80cm)^2} = -306e/24.6cm^2 = -12.4e/cm^2 (c) the charge will be divided by the surface area surface area is 4Pi r^2 -306e/{4Pi(2.10cm)^2} = -306e/55.4cm^2 = -5.52e/cm^2 (d) the charge will be divided by the volume the volume of a sphere is (4/3)Pi r^3 -306e/{(4/3)Pi(4.00cm)^3} = -306e/268.1cm^3 = -1.14e/cm^3

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