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Electric Field
Define the concept of a field
A field is an area or volume that has a
number, representing some quantity,
assigned to every location.
That number can be a scalar
or a vector.
A football field has
numbers assigned in
one dimension
A weather map is an example of a
scalar field.
Every point on
the map has a
scalar quantity
associated with
it. In this case,
it’s temperature.
For example, the
temperature in NP is
about 75o
Vector Field Examples - Has an amount and a
direction associated with each position.
“Action at a distance”
• The electric force is another force that is able to
act at a distance. (Just like gravity)
• Electric charges don’t need to be touching to exert
a force on each other.
• This means the electric force must be a field force.
Electric Field
• All charges create an electric field around
themselves.
• Any other charge in that electric field will
experience an electric force & will either be
attracted or repelled by the original charge.
• It is this electric field that extends out around
a charge that allows that charge to act at a
distance on another charge.
This is similar to a gravitational field.
Any object near the
surface of the Earth
will accelerate
towards the Earth at
9.8 m/s2
Any object that is
3.8x108 m from
the surface of the
Earth will
accelerate
towards the Earth
at 0.00272 m/s2
Only charges are more complicated.
• Masses only attract so all gravitational fields
point towards the mass creating them.
• Charges can both attract and repel. So the
field might point towards a charge or away
from the charge creating the field, depending
on its charge.
Test Charge
• To determine the direction of the electric
field, a test charge is used.
• A test charge is a pretend positive point
charge that is infinitely small and has a very
very small positive charge so it will not disrupt
the field it is in at all.
• The test charge is always positive, never
negative.
Draw the electric field around a positive charge.
Electric field for a positive charge
+
Draw the electric field for a negative charge.
Drawing Electric Field Lines
1. The lines must begin on positive charges
and end on negative charges, or at infinity.
2. The number of lines drawn leaving a
positive charge or approaching a negative
charge is proportional to the amount of
charge.
3. Field lines may not cross or touch each
other.
This implies that the
vector sum has two
values---which it can’t
4. Field lines must meet conductors or
charges perpendicular to the surface of the
conductor or charge.
Example: 2 Charges
Example: Charge & Plate
This is an
equipotential
line. Do not worry
about it for now.
Back to Earth’s Gravitational Field:
Mass CREATING
Near the surface of the Earth, Earth’s gravitational
the fieldfield
is 9.8 N/kg downwards, toward Earth’s surface.
Mass EXPERIENCING
Do larger masses experience
a larger gravitational field
the field
from Earth?
What two variables does gravitational field depend on?
æ GM 2 ö
GM1M 2
Fg =
= M1 ç 2 ÷ = mg
2
è R ø
R
Calculation of a Gravitational
Field (on Earth 9.8 m/s2)
It is the same thing
with electric fields
This charge EXPERIENCES
the field
 kQ1Q2
F
2
d
This charge CREATES
According to
Coulomb’s Law:
 kQ
F 2 Q
d
the field
This part of
Coulomb’s Law
calculates the
Electric Field (E)
The electric field produced by a point or spherical charge
is given by….
The direction of the
 kQ
E 2
d
electric field is
based on the
direction of force
for a positive
charge.
K = Coulomb’s Constant (9.0x109 N m2/C2)
Q = The charge producing the field.
Coulombs
Given in
d = The distance to the point in question
Q
Another way to
calculate electric force
is this:
This charge EXPERIENCES
the field
 kQ1Q2
F
2
d
This charge CREATES
According to
Coulomb’s Law:
 kQ
F 2 Q
d
the field
Another way to
calculate electric
force is this:
 
F  EQ
E
(electric field)
Another way to calculate electric force:
 
F  EQ
• F = Electric Force (N)
• E = Electric Field (N/C)
• Q = Charge placed in the
electric field (C)
Very
similar to
Fg = mg
What is the electric field 20.00 m to the right of a
(+) 0.0025 C point charge?
+
.0025 C
20.00 m
E=?
 kQ
E 2
d
9.0 ´10 9 (.0025C )
E=
2
2
20.00 m
= 5.6x104 N/C
Two charges are along the x-axis. Q1 is 3.0 m from the origin and
has a charge of -12.0mC. Q2 is 4.5 m from the origin and has a
charge of +4.0mC. (all charges are along the positive x-axis)
a) Calculate the electric field 8.0 m from the origin.
0.0 m
kQ1
E1 = 2
d1
3.0 m
4.5 m
8.0 m
-
+
E=?
Q1 = - 12.0x10-6C
-6
(9 ´10 )(-12.0 ´10 )
E1 =
5.0 2
9
E1 = 4320N / C
kQ2
E2 = 2
d2
(9 ´10 9 )(+4.0 ´10-6 )
E2 =
3.52
Q2 = + 4.0x10-6C
E2 = 2939N / C
0.0 m
4.5 m
3.0 m
+
Q1 = - 12.0x10-6C
Q2 = + 4.0x10-6C
E1 = 4320N / C
E2 = 2939N / C
=
ETotal =1400N / C
8.0 m
E=?
b) What force will a - 9.0 mC charge experience if it
is placed 8.0 m from the origin?
0.0 m
3.0 m
4.5 m
-
+
Q1 = - 12.0x10-6C
Q2 = + 4.0x10-6C
8.0 m
Q3 = - 9.0x10-6C
E = 1381 N/C 
F = QE
F = (-9.0x10-6C)(1380N/C)
F = 0.012 N
Two charges, +Q and –Q, are located two meters apart
as shown. Which vector best represents the direction
of the electric field at the point above them?
2
3
1
4
+
-
Two charges, +Q and –Q, are located two meters
apart as shown. Which vector best represents
the direction of the electric field at the point
above them?
3
+
-
Two point charges, separated by 1.5cm, have charges of
+2 and -4C. Suppose we determine that 10 field lines
radiate out from the +2C charge. If so, what might be
inferred about the -4C charge with respect to field lines?
1) 20 radiate out
4) 10 radiate in
2) 5 radiate out
5) 5 radiate in
3) 20 radiate in