1. Section 4.1.3 of Griffiths contains a discussion of the electric field acting on a polar molecule.

For simplicity, let's assume that a polar molecule can be approximated by a dipole moment p.

Compare two cases:

a) A polar molecule with dipole moment p in the homogeneous electric field E.

b) A polar molecule with dipole moment p in an inhomogeneous electric field (electric field

varies in space) E.

Derive the force acting on this molecule in both cases.

2. Imagine that you have a high-quality homogeneous isotropic linear dielectric (HfO₂) with

dielectric constant &r= 25. Using the solution of Example 4.7 of Griffiths calculate the change

of electric field inside the sphere made of such HfO₂ that is put in external homogeneous

electric field Eo. Note that there is no free charge placed on the sphere.

3. For the same dielectric as in the previous example (HfO₂ with dielectric constant &, = 25),

imagine that a fixed free charge density pf is placed inside such dielectric. Derive the

relationship between bound and free charge density inside such dielectric.

4. Calculate the bound charge density p, inside the material with constant polarization P.