Chapter 21 : Electric Charge and Electric Field

Electric Dipole

Charges rarely appear alone, so let's look at a particular configuration that appears frequently in molecular interations (i.e. chemistry): the electric dipole where we have two identical but oppositely charges separated by some distance.
Even though the dipole is overall electrically neutral, it will still exert a force on charges nearby, as we'll see.

The left figure above shows a model of a chlorine molecule Cl₂
Each chlorine atom has 7 of the 8 electrons needed to fill it's outermost shells, and it can 'fix' that by sharing an electron with another atom.
In the middle figure, a chlorine atom is sharing an electron with a hydrogen atom, but looking at the electronegativity chart from the previous lecture, chlorine 'wants' the electron much more than the hydrogen atom. The shared electron here spends more time associated with the chlorine atom than with the hydrogen atom, causing the chlorine 'side' of the molecule to have a slight net negative charge, leaving the hydrogen side of the molecule having a slight net positive charge.
The figure on the right is an even more extreme case. Here we see a NaCl molecule (salt). Again, looking at the electronegativity chart, the difference between sodium and chlorine is very large. Here, the electron isn't really shared, but is removed from the sodium atom and transferred to the chlorine atom, leading to an even clearer dipole character: the Na atom has a net +1e charge, and the Cl atom has a net -1e charge.

Suppose we have charges of +Q and -Q separated by some distance d and we want to find what force those exert on some other charge q that's located some distance x away (along a line that passes through the midpoint between the original charges and is perpendicular to that line; the fancy way of saying this is our new charge q is along the perpendicular bisector.

Assuming q is positive, this figure shows the electric force vectors that the +Q and -Q charges will be exerting on it.
The net force acting on q will be the vector sum of those forces.

We'll work through this in class and find there is a net force on that loose charge, and in an unexpected direction...

As we move the location of our little test charge 'q', the vector electric forces will change in magnitude and direction.
A useful way of thinking about this is to look at something called the ELECTRIC FIELD.

FIELDS : Gravity

The force approach to analyzing two interacting objects is to think of the mutual force each is exerting on the other: two masses gravitationally attract; two charges either repel or attract each other depending on whether the charges are of the same or opposite sign, and so on.
The field approach is to say that the first object creates a field around it (gravitational, or now electric) which in a sense is already 'there' whether the second object is present or not. Then when the second object is introduced, it will feel a force due to that field. (And that new object introduces it's own field which is what the first object now reacts to.)
Let's go through this 'field' process with gravity first.
Suppose we have a mass m₁ (maybe it's the Earth) and another mass m₂ (maybe the Moon) in the area. What force of gravity will the Earth be exerting on that other mass?
Let's put a different mass (maybe a satellite) somewhere else. What force of gravity will the Earth be exerting on the satellite?

Gravitational Field \( \vec{g} \) around a mass
This is a 3-D 'graph' of \( \vec{g} \) as it changes in magnitude and direction.
The force on another object will be it's mass times the field created by the first object: \( \vec{F} = m \vec{g} \)

Illustration of radial unit vectors. Note \( \hat{r} \) just means pointing radially away from a point, regardless of any other consideration.

FIELDS : Electric Field

The (gravitational) field \( \vec{g} \) is essentially the (gravitational) force per mass on some other object: \( \vec{g} = \vec{F}_g / m \).
We can go through the same process with the electrical force equation and rearrange terms the same way we did with gravity.
The force that object 1 (of charge Q) exerts on object 2 (of charge q) is equal to the charge on object 2 (q) times the electric field created by object 1:
\( \vec{F} = q\vec{E} \) where \( \vec{E} = k\frac{Q}{r^2}\hat{r} \) for example.
Since E is the force/charge, the units of E will be Newtons/Coulomb.
(Later on, we'll find a more convenient unit is also volts/meter, but we'll need to learn about volts first!)

I'll follow this link for some figures of electric fields around pairs of charges.

Electric Dipole
Charges rarely appear alone, so let's look at a particular configuration that appears frequently in molecular interations (i.e. chemistry): the electric dipole where we have two identical but oppositely charges separated by some distance. Even though the dipole is overall electrically neutral, it will still exert a force on charges nearby, as we'll see.
The left figure above shows a model of a chlorine molecule Cl₂ Each chlorine atom has 7 of the 8 electrons needed to fill it's outermost shells, and it can 'fix' that by sharing an electron with another atom. In the middle figure, a chlorine atom is sharing an electron with a hydrogen atom, but looking at the electronegativity chart from the previous lecture, chlorine 'wants' the electron much more than the hydrogen atom. The shared electron here spends more time associated with the chlorine atom than with the hydrogen atom, causing the chlorine 'side' of the molecule to have a slight net negative charge, leaving the hydrogen side of the molecule having a slight net positive charge. The figure on the right is an even more extreme case. Here we see a NaCl molecule (salt). Again, looking at the electronegativity chart, the difference between sodium and chlorine is very large. Here, the electron isn't really shared, but is removed from the sodium atom and transferred to the chlorine atom, leading to an even clearer dipole character: the Na atom has a net +1e charge, and the Cl atom has a net -1e charge.
Suppose we have charges of +Q and -Q separated by some distance d and we want to find what force those exert on some other charge q that's located some distance x away (along a line that passes through the midpoint between the original charges and is perpendicular to that line; the fancy way of saying this is our new charge q is along the perpendicular bisector.
Assuming q is positive, this figure shows the electric force vectors that the +Q and -Q charges will be exerting on it. The net force acting on q will be the vector sum of those forces. We'll work through this in class and find there is a net force on that loose charge, and in an unexpected direction...
As we move the location of our little test charge 'q', the vector electric forces will change in magnitude and direction. A useful way of thinking about this is to look at something called the ELECTRIC FIELD.