In this video we briefly introduced the idea of electric field and then we're going to work a
couple examples of calculating an electric field and calculating a force due to an electric field
so we start with this isolated positive point charge and we're going to call this the source
charge and coulomb's law says that this source charge would exert a repulsive force on any
positive charge in the vicinity so i'm going to just draw one real quick and we would normally
call that second charge the test charge it's the one that we're using to feel what the original
source charge is doing so if there was a test charge in the vicinity it would be pushed away
from that source charge but what if there isn't a test charge in the neighborhood of this source
charge hopefully you agree that there should still be something going on around this source charge
and the idea is that the space around the source charge is filled with an electric field that
would exert an electric force if we introduced a charge the direction of that electric field
is given by the direction the force would point on a positive test charge so it looks like this
again that electric field is pointing away from the source charge because that's the direction of
force would be applied to a positive test charge if one happened to be there one thing i want to
point out before getting quantitative with this is that you can see the spacing of the field lines
becomes denser as i get closer to that positive charge and that's a way of saying the electric
field is stronger there in other words the force on a positive charge would be greater there so to
get quantitative about electric field i can say the electric field is the force per unit charge
and our units of electric field
would then be newtons per coulomb turning this around i can say the electric force on a test
charge is given by the magnitude of that test charge multiplied by the electric field vector
so i can see from the second equation that if i doubled the magnitude of the test charge it would
then double the force experienced by the test charge so on the left hand side of this slide
i want to figure out what's a formula for the electric field surrounding a point charge now
we are going to look at other distributions of charge besides just a point charge but this
one comes up a lot so i want to find the electric field in the space surrounding this source charge
so quoting the definition of the electric field as the force
per unit charge felt by a test charge that q would be q tests well coulomb's law gives me
a way of writing the force between the two charges so that's going to be k q source
q test
over the distance between them squared
and then i'm dividing that by the magnitude of the test charge right so the test charge is going to
cancel out of this thing and it gives me a formula for the electric field surrounding a point charge
that allows us then to answer a question like this first example
compute the electric field at a distance of one meter from a one micro coulomb charge
all right so we could go in any direction to do this as long as we're one meter away from that
source charge and the electric field is going to be a vector assigned to each point in space
again pointing away from this positive source charge because that's the direction the force
would be on a positive test charge then we apply our formula real quick
the electric field generated by a point source is going to be kq over r squared
and we plug in the numbers the coulomb's law constant is eight point nine nine times ten
to the ninth newton meters squared per coulomb squared the magnitude of our source charge is
one micro coulomb which is ten to the negative six coulombs and the distance between the source
charge and the point that we're interested in is one meter and when i run the numbers i get 8990
and the units of electric field again that's units of force divided by units of charge so that's
newtons per coulomb another way to describe this is that if you were to put one coulomb of charge
at that point one meter away from our source charge it would feel a force of 8990 newtons
let's look at a more reasonable magnitude of charge though we're going to put an electron
at this location and an electron has a charge of negative qe if i'm keeping track of sines where qe
is the elementary charge and i get negative 1.6 times 10 to the negative 19 coulombs for that
and once i have an electric field it's very simple to find the force that it exerts
on a test charge you just multiply the charge of the test charge by the electric field at that
point in space so that's really just turning this original formula for e around and i write
f equals q e now if i keep my minus sign then it indicates that i have an attractive force going on
alternatively you can just make better diagrams and do all your calculations in
terms of magnitudes instead of keeping the signs but i'll go ahead and keep that minus
sign this time so i have negative 1.6 times 10 to the negative 19 that's the charge on the electron
multiplied by the strength of my electric field there
i'll go ahead and show you what's going on with the units the coulombs cancel and i get newtons
so i get a force of negative indicating that it's an attractive force 1.44 times 10 to
the negative 15 newtons on this electron that might seem like it's an incredibly small force
but the mass of an electron is incredibly small so the acceleration would be enormous
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