Question

Density, density, density. (a) A charge -321e is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 72^o. What is the linear charge density along the arc? (b) A charge -321e is uniformly distributed over one face of a circular disk of radius 2.10 cm. What is the surface charge density over that face? (c) A charge -321e is uniformly distributed over the surface of a sphere of radius 4.30 cm. What is the surface charge density over that surface? (d) A charge -321e is uniformly spread through the volume of a sphere of radius 3.70 cm. What is the volume charge density in that sphere? ( SHOW ALL WORK)

Answer 1

Linear charge density = charge/length of arc
length of arc = angle in deg. *pi* R / 180
R is radus of arc.
Linear charge density, = -321*1.6x10^-19 / (72*3.14*4/180)   
                                     = - 1.02x10^-17 C/cm

b) Area of disk = pi R² = 3.14*2.1² = 13.85 cm²
Surface charge density, = -321*1.6x10^-19 / 13.85 = -3.7x10^-18 C/cm²

c) Surface area of sphere = 4 pi R² = 232.23 cm²
Surface charge density, = -321*1.6x10^-19/ 232.23 = -2.2x10^-19 C/cm²

d) Volume of the sphere = 4 pi R³/3 = 212.1 cm³
Volume charge density, = -321*1.6x10^-19/ 212.1
                                        = 2.4x10^-19 C/cm³