Transcript Imagine a universe where the force of gravity is repulsive, not

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
We can also define a field in
terms of vectors.
He learned this in our
school!
Vector Field Examples - Has an amount and a
direction associated with each position.
Example: Earth has a
Gravitational Field
The Electric Field (E) is a vector field
• Any charge will set up an electric field around
it.
•It exerts an electric force on any other
charged object within the field.
•It is defined as the force per positive charge.
Don’t confuse the charge that creates
the field with the charge that reacts to the
field
Look at phet “Charges and Fields”
All electric charges set up an electric field around
themselves. To determine the direction of an
electric field at any given point, a positive point
charge or test charge is used.
A positive point charge is like a point or an
infinitely small spot that has a single positive
charge.
Convention states that when testing an electric
field, always use a positive point charge, never a
negative one.
Electric Fields are always tested with positive
point charges.
Remember: Positive Point charges come from
your Pants Pocket
+
Draw the electric field around a positive charge.
Electric field for a positive charge
+
Draw the electric field for a negative charge.
Drawing Electric Fields
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
Less Charge
Example: Charge & Plate
This is an
equipotential
line. Do not
worry about it
for now.
Q
Back to Earth’s
Gravitational Field:
Mass CREATING
the field
Near the surface of the Earth, Earth’s gravitational
field is 9.8 N/kg
downwards,
toward Earth’s surface.
Mass
EXPERIENCING
the fielda larger gravitational
Do larger masses experience
field from Earth?
What two variables does gravitational field depend on?
GM 2 
GM 1M 2
Fg 
 M 1  2 
2
 R 
R

Calculation of a
Gravitational Field (on
Earth 9.8 m/s2)
Consider a positive charge in
space.
+
The Electric Field is used to
describe the effect of this
charge at some point in space.
Consider a positive charge in
space.
+
+
10 N
If a positive point charge (+1) is
placed at that point, a force will
be exerted on it by the original
charge.
Let’s say, the force is 10 N.
Consider a positive charge in
space.
E = 10 N/C
+
Then we can say, whenever a charge is
placed at that point, for every coulomb of
charge, it will have a force of 10 N act on it.
We say the electric field at that
point is 10 N per coulomb.
Consider a positive charge in
space.
+
If a 3 C charge is placed there, the
force on it would be 3 C x 10 N/C or
30 N.
In general, we say F = Q E
Another equation
for EXPERIENCES
This charge
the field
Electric Field:
 kQ1Q2
F
2
d
This charge
According to
Coulomb’s Law:
Another way to
CREATES the
calculate
electric force is
field
this:
 
F  EQ
 kQ
F 2 Q
d
Therefore, this
part of Coulomb’s
Law must
calculate the
Electric Field
Q
The electric field produced by a point or
spherical charge is given by….
The direction of
 kQ
E 2
d
the 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.
Given in Coulombs
d = The distance to the point in question
Q
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 .0025C 
4 N/C
E
=
5.6x10
2
2
20.00 m
9
Q
The electric field produced by a point charge is 16
N/C at a distance of 10. m. At what distance will the
field be 4.0 N/C?
1) 20.m
2) 5.0m
3) 25m
4) 40.m
5) 32m
The electric field produced by a point charge is 16
N/C at a distance of 10.m. At what distance will the
field be 4.0 N/C?
1) 20.m
2) 5.0m
3) 25m
4) 40.m
kQ
E 2
d
N (9.0 10 9 Nm 2 /C 2 )Q
16 
2
C
(10.m)
7
Q  1.77810 C
5) 32m
N (9.0 10 Nm /C )(1.77810 C)
4.0 
2
C
d

d  20.m
9
2
2
7
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?
1
2
3
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
2
above them?
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?
+
-
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
3.0 m
-
Q1 = - 12.0x10-6C
4.5 m
+
Q2 = + 4.0x10-6C
8.0 m
E=?
0.0 m
3.0 m
-
Q1 = - 12.0x10-6C
4.5 m
+
Q2 = + 4.0x10-6C
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
4.5 m
3.0 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 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
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