# The Electric Field

```Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
Coulomb’s Law:
it’s just part of a bigger picture
Coulomb's Law quantifies the interaction between charged
particles.
1
F =
12 4πε
0
q 1q 2
2
12
r
r12
,
+
-
Q1
Q2
Charged particles exert forces on each other over great
distances.
How does a charged particle "know" another one is “there?”
We use the concept of an electric field to explain this
interaction. Here's the idea…
The Electric Field
F12
 A charged particle propagates (sends
out) a "field" into all space.
 Other charged particles
sense the field, and “know”
that the first one is there.
+
+
like
charges
repel
A charged particle modifies the
properties of the space around it.
F21
F13
F31
unlike
charges
attract
The idea of an electric field is good for a number of reasons:
 It makes us feel good, like we’ve
actually explained something.
OK, that was a flippant remark. There are serious reasons
why the idea is “good.”
 We can develop a theory based on this
idea. From this theory may spring
unimagined inventions.
If the theory explains past observations and leads to new
predictions, the idea was “good.”
 The electric field is real!
F12
+
F13
F31
+
F21
like
charges
repel
unlike
charges
attract
Trust me. Or go stand outside in an electric storm and then
try to tell me the electric field is not real.
Some physicists will tell you the electric field is real. Others disagree. It seems to depend on what you define “real” to mean.
We define the electric field by the force it exerts on a test
charge q0:
E =
F0
The subscript “0” reminds you the force is on the
“test charge.” I won’t require the subscripts when
you use this equation for boardwork or on exams.
q0
If the test charge is "too big" it perturbs the electric field, so the
“correct” definition is
E = lim
q0  0
F0
q0
You won’t be required to use
this version of the equation.
Any time you know the electric field, you can use this equation to calculate the force
on a charged particle in that electric field: F = qE
This version of the electric field equation is on your equation
sheet. Use it for problems involving electric fields and forces:
I’m not mad, I tell you, not mad. The
little voices tell me I’m quite sane.
F = qE
This is your second starting equation. The equation tells you the direction of the
electric field is the direction of the force exerted on a POSITIVE test charge. The
absence of absolute value signs around q means you MUST include the sign of q in
 F0 
N


E  =
=
 
q 0  C
The units of electric field are
newtons/coulomb.
In chapter 3, you will learn that the units of electric field can
also be expressed as volts/meter:
E 
=
N
C
=
V
m
The electric field can exist independent of whether there is a
charged particle around to “feel” it.
Remember: the electric field direction is the
direction a + charge would feel a force.
+
A + charge would be repelled by another + charge.
Therefore the direction of the electric field is away from
positive (and towards negative).
http://regentsprep.org/Regents/physics/phys03/afieldint/default.htm
Gravitational Fields
The idea of a field is not new to you. You experienced fields
(gravitational) in Physics 1135.
FG =G
g( r) =
m 1m 2
2
12
, attractive
r
FG
m
Units of g are
actually N/kg!
g( r) is the local gravitational field. On earth, it is about 9.8
N/kg, directed towards the center of the earth.
A particle with mass modifies the properties of the space around it.
If the last equation
looks like this, you
have missing fonts.
Lecture 1 agenda:
Electric Charge.
Just a reminder of some things you learned back in grade school.
Coulomb’s Law (electrical force between charged particles).
You must be able to calculate the electrical forces between one or more charged particles.
The electric field.
You must be able to calculate the force on a charged particle in an electric field.
Electric field due to point charges.
You must be able to calculate electric field of one or more point charges.
Motion of a charged particle in a uniform electric field.
You must be able to solve for the trajectory of a charged particle in a uniform electric field.
The Electric Field
Due to a Point Charge
Coulomb's law says
F =k
12
q 1q 2
2
12
,
r
... which tells us the electric field due to a point charge q is
E q =k
q
r
2
, aw ay from +
…or just…
E=k
q
r
This is your third starting equation.
2
E=k
q
r
2
A physics 2135 equation is like a toaster!
You wouldn’t shove
yogurt down your
toaster, would you?
You can’t expect to just shove numbers into an equation and
out pops the correct answer.
To experience the optimum user satisfaction from your physics
2135 toaster equations you need to understand what they
mean and think about what you are doing with them.
If we define rˆ as a unit vector from the source point to the field
point…
source point
rˆ +
field point
…then the equation for the electric field of a point charge
becomes:
E =k
q
r
2
rˆ
Consult a professional before using. Do not use more
than 4 times a day without seeing your physicist.
May cause headaches, dizziness, and upset stomach.
Drink a full glass of water with each use.