Electric Fields in Matter

Question 1

In general, the two ways that an electric field can distort the charge distribution of an atom or molecule are…

Answer 1

…stretching and rotating

Question 2

What happens if an atom is placed in an electric field?

Answer 2

The nucleus is pushed in the direction of the field, and the electron cloud is pushed in the opposite direction, causing the atom to stretch until the electrostatic attraction is in equilibrium with the external field. The atom thus develops a dipole moment p in the direction of the field.

Question 3

The dipole moment vector (for a physical/real dipole) is equal to:

Answer 3

the charge (q) of one end of the dipole multiplied by the distance (d) vector going from negative to positive

Question 4

When an atom is exposed to an electric field, how is the dipole moment induced in the atom related to the strength of the electric field?

Answer 4

Proportionately, with a proportionality constant called the “atomic polarizability”.

p = aE

Question 5

With regard to polarization, how are molecules different than atoms?

Answer 5

Molecules may polarize more in certain directions than others. For example, a linear molecule like Carbon Dioxide is polarized more easily along the axis of the molecule than perpendicular to it.

Question 6

When calculating the induced dipole moment of a linear molecule (e.g. CO2) exposed to an external electric field, what do you do if the electric field isn’t along the axis of the molecule?

Answer 6

You have to decompose the electric field into components parallel and perpendicular to the axis of the molecule, then multiply each by their corresponding polarizability constants, and add them up vectorially.

Question 7

The dipole moment vector points from…

Answer 7

…negative to positive

Question 8

What is the force on a dipole exposed to a uniform electric field?

Answer 8

None. Since the field is uniform, the force on the positive and negative ends cancel out.

Question 9

In general, the action of an electric field on a dipole is to…

Answer 9

…align the dipole moment vector with the electric field.

Question 10

What is the formula for the torque on a dipole due to a uniform electric field?

Answer 10

The torque on a dipole is equal to the cross product of the dipole moment and the electric field.

N = p x E

Question 11

A non-uniform electric field will act on a dipole with…

Answer 11

torque and a net force.

Question 12

What is the formula for the net force on a dipole in a non-uniform electric field?

Answer 12

The force is equal to q times delta-E, the change in the electric field across the dipole.