Question

Density, density, density. (a) A charge -305e is uniformly distributed along a circular arc of radius 5.20 cm, which subtends an angle of 64o. What is the linear charge density along the arc? (b) A charge -305e is uniformly distributed over one face of a circular disk of radius 2.90 cm. What is the surface charge density over that face? (c) A charge -305e is uniformly distributed over the surface of a sphere of radius 3.40 cm. What is the surface charge density over that surface? (d) A charge -305e is uniformly spread through the volume of a sphere of radius 4.70 cm. What is the volume charge density in that sphere?

Answer 1

Q = -305e
= -305*1.6e-19 (C)
= 4.88e-17 (C)

1) R = 5.2 (cm) = 5.2e-2 (m), angle = 64 degrees = 64*pi/180
The length is = 5.2e-2 * 1.11 = 5.57e-2 (m) , so the linear charge density is:
4.88e-17/5.576e-2 = 8.75*10^-16 C/m

2) Disk of radius 2.9 (cm) = 2.9e-2 (m)
The area is pi*r^2 = pi*8.41e-4 so the surface charge density is:
4.88e-17/(pi*8.41e-4) =1.84*10^-14 (C/m^2)

3) Sphere of radius 3.4 (cm)
The area is 4*pi*r^2 = 4*pi*11.56e-4 ;so the surface charge density will be
4.88e-17/ 4*pi*11.56e-4 = 3.35*10^-15 C/m^2


4)r = 4.7 cm
The volume is 4*pi*r^3/3 = (4*pi*103.823/3)*e-6 , so the charge density is:
4.88e-17/( (4*pi*103.823/3)*e-6) = 1.12*10^-13 C/m^3