Density, density, density. (a) a charge -301e is uniformly distributed along a circular arc of radius 5.60 cm, which subtends an angle of 53o. what is the linear charge density along the arc? (b) a charge -301e is uniformly distributed over one face of a circular disk of radius 4.80 cm. what is the surface charge density over that face? (c) a charge -301e is uniformly distributed over the surface of a sphere of radius 5.20 cm. what is the surface charge density over that surface? (d) a charge -301e is uniformly spread through the volume of a sphere of radius 4.10 cm. what is the volume charge density in that sphere?

(a): Linear charge density of the circular arc =

(b): Surface charge density of the circular arc =

(c): Volume charge density of the sphere =  

Explanation:

Part (a):

Given:

We know, e is the elementary charge whose value is

Therefore,

Also, the length l of a circular arc is given as:

The linear charge density of the arc is defined as the charge in the unit length of the arc.

Part (b):

Given:

Surface area of the circular disc,

The surface charge density of the disc is defined as the charge in the unit area of the disc.

Part (c):

Given:

Volume of the sphere,

The volume charge density of the sphere is defined as the charge in the unit volume of the sphere.