The electric field describes the effect of a charge, or set of charges,
on the region surrounding it. The electric field, **E**, at any
point in space is a vector that represents the force, **F**, on a
small positive test charge, q, with magnitude:

**E** = **F**/q

The electric field due to a
positive
charge extends radially **out** in
all directions from the charge (because a positive test
charge placed near it would feel a force pointing away from it).
The electric field due to a
negative
charge points radially **in** from
all directions (because a positive test charge placed near
it would feel a force pointing toward it). In general, electric field
lines always point **from positive** charges and **toward negative**
charges.

Consider a dipole: two charges of equal magnitude and opposite sign separated by a distance, d. What do you think the field will look like for this configuration? You can check your prediction using the simulation by recalling that if you double click on a point, the field line going through that point will be plotted. Do this for a sufficient number of points so that you have a good idea of what the field looks like.

Notice that every field line that leaves the positive charge ends on the negative charge. That is, there are just as many field lines surrounding the positive charge as the negative charge.

Now consider a configuration of two unequal charges separated by a distance, d. Construct the field lines again. Do you notice anything different?

The field lines still go from positive to negative but the number of lines surrounding the positive and negative charges differ. There are more lines leaving the positive charge than ending on the negative charge. This is because the magnitude of the positive charge is larger than the negative charge. In fact, the **number of field lines starting on a positive charge, or ending on a
negative charge, is proportional to the magnitude of the charge.**

In the above simulation, what is the ratio of the two charges?

Just like forces, electric fields obey the principle of superposition, which
says that the **net** electric field due to a set of charges is the
**vector** sum of the electric fields from each of the individual charges.
That is:

**E**_{net} =
**E**_{1} +
**E**_{2} +
**E**_{3} +...

Consider the case of a
dipole again.
When you look in the region immediately surrounding the positive charge, the
field lines appear to be pointing radially outward just like the single
positive charge you saw above. This is because the field here is dominated by the
positive charge so the contribution from the negative charge is negligible.
(**E**_{net} = **E**_{+} + **E**_{-} with
E_{+} much larger than E_{-}.) Away from both charges, where
both charges make significant contributions to the net field, the field lines
begin to curve due to the vector nature of the sum of the two fields.

In Milestone 3, if the square is 4 cm on a side, what is the magnitude of each charge?

Answers to questions:

- 2:1
- 2.2 x 10
^{-10}C

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