Polarization

A stationary point charge $+Q$ is near a block of polarization material (a linear dielectric). The net electrostatic force on the block due to the point charge is:

1. attractive (to the left)
2. repulsive (to the right)
3. zero

The sphere below (radius $a$) has uniform polarization $\mathbf{P}_0$, which points in the $+z$ direction. What is the total dipole moment of this sphere?

1. zero
2. $\mathbf{P}_0 a^3$
3. $4\pi a^3 \mathbf{P}_0/3$
4. $\mathbf{P}_0$
5. None of these/must be more complicated

The cube below (side $a$) has uniform polarization $\mathbf{P}_0$, which points in the $+z$ direction. What is the total dipole moment of this cube?

1. zero
2. $a^3 \mathbf{P}_0$
3. $\mathbf{P}_0$
4. $\mathbf{P}_0/a^3$
5. $2 \mathbf{P}_0 a^2$

In the following case, is the bound surface and volume charge zero or nonzero?

1. $\sigma_b = 0, \rho_b \neq 0$
2. $\sigma_b \neq 0, \rho_b \neq 0$
3. $\sigma_b = 0, \rho_b=0$
4. $\sigma_b \neq 0, \rho_b=0$

In the following case, is the bound surface and volume charge zero or nonzero?

1. $\sigma_b = 0, \rho_b \neq 0$
2. $\sigma_b \neq 0, \rho_b \neq 0$
3. $\sigma_b = 0, \rho_b=0$
4. $\sigma_b \neq 0, \rho_b=0$