1. Electric field generated by a spherically symmetrical distribution of charge.
(a) Using Gauss' law and the Curie principle, find the electric field as a function of the distance to the
center of the charge distribution.
(b) Application to a uniformly charged sphere. What is the electric field inside the sphere, and outside
the sphere?
2. Using Gauss' law and the Curie principle find the electric field generated
\(\bullet\) by an empty sphere charged on its surface
\(\bullet\) in the spherical and empty cavity (radius $R_c$ centered in $O_2$) of a uniformly charged sphere (radius
$R_s$ centered at $O_1$). Do you notice anything remarkable?
3. Electric field generated by a linear and uniform distribution of charge.
A linear wire, if one neglects its diameter, can be characterized by its amount of charge per unit length.
What is the electric field created by this wire as a function of the distance
(a) Using Coulomb's law, calculate the electric field generated by this wire.
(b) Then using Curie's principle and Gauss' law, calculate the electric field and compare.
4. Uniformly charged infinite plane.
(a) What are the symmetries of the charge distribution. How do you choose the surface in order to
apply Gauss' law and find the E field.
(b) Calculate the E field using Gauss law.
(c) Recover the capacitance between two parallel electrodes facing each other at distance $d$ appart and
each with area $S$.