Simple Nature - Light and Matter

n/Example 5.

whereriis the position vector of the charge labeled by the index

i. We can then write the torque in terms of a vector cross product

(page 287),

τ=D×E.

No matter how we notate it, the definition of the dipole moment

requires that we choose a point from which we measure all the posi-

tion vectors of the charges. However, in the commonly encountered

special case where the total charge of the object is zero, the dipole

moment is the same regardless of this choice.

Dipole moment of a molecule of NaCl gas example 4

.In a molecule of NaCl gas, the center-to-center distance be-

tween the two atoms is about 0.24 nm. Assuming that the chlo-

rine completely steals one of the sodium’s electrons, compute the

magnitude of this molecule’s dipole moment.

.The total charge is zero, so it doesn’t matter where we choose

the origin of our coordinate system. For convenience, let’s choose

it to be at one of the atoms, so that the charge on that atom

doesn’t contribute to the dipole moment. The magnitude of the

dipole moment is then

D= (2.4× 10 −^10 m)(e)

= (2.4× 10 −^10 m)(1.6× 10 −^19 C)

≈ 4 × 10 −^29 C·m

The experimentally measured value is 3.0× 10 −^29 C·m, which

shows that the electron is not completely “stolen.”

Dipole moments as vectors example 5

.The horizontal and vertical spacing between the charges in the

figure isb. Find the dipole moment.

.Let the origin of the coordinate system be at the leftmost charge.

D=

∑

qiri

= (q)(0) + (−q)(bxˆ) + (q)(bxˆ+bˆy) + (−q)(2bxˆ)

=− 2 bqxˆ+bqyˆ

The dipole moment points up and to the left, which makes sense

because the positive charges are predominantly above and to the

left of the negative ones.

Molecules with zero and nonzero dipole moments example 6

It can be useful to know whether or not a molecule is polar, i.e.,

has a nonzero dipole moment. A polar molecule such as water

is readily heated in a microwave oven, while a nonpolar one is

not. Polar molecules are attracted to one another, so polar sub-

stances dissolve in other polar substances, but not in nonpolar

substances, i.e., “like dissolves like.”

586 Chapter 10 Fields