Gauss's law examples
Example 1
Use Gauss's law to find the electric field created anywhere in space by
a) a point charge Q (check your answer with Coulomb's law)
b) a sphere of charge Q uniformly distributed on the surface of the sphere (there is no
charge inside of the sphere). The radius of the sphere is R.
c) a solid sphere of charge Q uniformly distributed within the sphere. The radius of
the sphere is R.
d) a solid sphere of charge Q and radius R. The volume charge density within the
𝐶
sphere is 𝜌 = . where 0 ≤ 𝑟 ≤ 𝑅.
𝑟
e) an infinite line of charge of constant linear charge density λ (check your answer with
what we obtained using Coulomb's law).
Example 2
The electric field at the surface of the Earth is pointing down and is 100 N/C. What is the surface
charge density on the Earth?
Example 3
A neutral conductor is placed above a charged plate with positive surface charge density η.
Assume that the plate and the conductor are both very large (i.e. you may assume that they are
infinitely wide). What is the electric field in regions 1, 2, 3 and 4.
4
3
conductor
2
charged plate
1