Previously, we looked at the electric
field surrounding one particle. Now, let's
look at the electric field around two
particles. Let's say we have one positive
particle, and one negative particle next
to each other. Electric field lines
describe the force that a positive
particle will experience. To determine
the direction of the field lines, we will
analyse the direction of the force a
positive particle will experience. Let's
say we had a positive particle here. Then,
it would be pushed away from the
positive charge, and pulled towards the
negative charge. So, the particle would
experience a force to the right, and thus
the electric field would also point to
the right. Let's say you had a positive
particle here. Then, it would be pushed
away from the positive charge and pulled
towards the negative charge. However, this particle is closer to the positive
charge than the negative charge; and so
the force it experiences from the
positive charge is bigger than the force
it experiences from the negative charge.
So, overall the particle experiences a
force in this direction. Now, doing this
again for every single point around
these two charges. If we look at the
force that the particle experiences at
every single point, we can see the
electric field. Using field lines to
represent the electric field we would
see this picture.
The electric field surrounding two
oppositely charged particles looks like
the magnetic field surrounding a bar
magnet. Another way to think of this is
with vectors. Let's look at two
oppositely charged particles like before.
If there is a positive particle here,
then there is a force pushing it away
from the positive charge and our force
pulling it towards the negative charge.
Using vector addition we get the total
force this positive particle will
experience. This is the vector field
representation of the electric field
around a positive particle; and the
electric field around a negative
particle looks like this. If we add up
the vectors at a point, we get the total
force a positive particle experiences at
that point. Now, we do this for all points
around the charges and we get the
electric field lines surrounding the
charges. The vector field representation
of electric fields can be confusing to
look at and understand at a glance. This
is why we also use a field line
representation. The field lines are
actually constructed from vector
addition of the electric fields of
individual interacting particles. Again,
looking at the force a positive particle
will experience, except this time we have
two negative charges. At the middle, a
positive particle will be attracted to
both negative charges equally, and so
there is no net force on it at this
location. But since electrostatic
attraction increases as distance
decreases, moving slightly to the left,
then the positive particle would
experience a force to the left. Moving up
slightly will still cause the positive
particle to be attracted equally to both
negative charges. However, there will be a
pull downwards
as the attraction to both negative
charges don't cancel out. Analyzing some
other points, we get the electric field
with the vector representation. And this
is the field line representation.
Analyzing it in terms of vector addition,
we have a force to the left from the
left negative charge, and a force to
the right from the right negative charge.
Adding the vectors we get a force
pointing down. Thus, a positive particle
at this location will experience a force
pushing it downwards. So there is an
electric field
pointing downwards at this location.
We can do the same analysis for the other
points.
Hence, the final electric field of these
two negative charges will look like this:
the vector representation, and the field
line representation. No matter how you
analyse the situation, you'll still get
the same result.
