Transcript 3 - BYU Physics and Astronomy

Math review
• In packet
– Study formulas and chapter summaries
– Study “What does it mean to integrate?”
Next two class periods we will do a lot of math review.
The math review test starts next Wednesday
Discussion question: Three charges are placed
as shown. Charges A and B are held fixed in
place. What direction is the force on C?
A
C
B
+q
+q
-q
A.
B.
C.
D.
E. Zero magnitude – no direction
Electric Field
• The direction of the Electric field is the direction of the
force on a positive point charge at a given point.
• Force is a vector
• Electric field is a vector
q1 feels a force due to an electric field produced by q2.
 kq1q2

F  2 rˆ  q1 E2
r
Three charges are placed as shown. Charges A
and B are held fixed in place. What direction
is the electric field at C?
A
C
B
+q
+q
-q
A.
B.
C.
D.
E. Zero magnitude – no direction
Can there be an electric field at a point where there is no charge?
●no. A charge must exist in order for an electric charge field to exist.
●Yes an electric field emanates from a charge, therefore at some point where
there is no charge there can be a field caused by a nearby charge.
●Yes, There can be an electric field at a point where there is no charge. The
electric field is the region of space around a charged object. So all points in
this region have the electric field but not necessarily a charge. (although it may)
●Yes, there can be an electric field at a point where there is no charge because
similar to the gravitational field, the gravitational field is there regardless of
wither or not there is an object there to "feel" that field. The electric field is
similar, there does not need to be a charge there to "feel" the field in order for
the field to still be there
●I think the first part of the question leaves room for a double meaning.
In one sense, it seems to ask: Can an electric field exist without a
source charge, in another sense, it sounds like it is asking: if a source
charge exists can there be a field without the presence of a test
charge? Well, for the former: No, because the charge is what creates
the field. If the later: yes, because the test charge just proves the
presence of the field, but doesn't create it.
Can there be a charge at a place
where there is no field?
• A charge is always in the middle of a field that it
creates so wherever there is a charge, at that
point there will also be a field.
• There can also be a charge where there is no
field because it will feel no force.
• Could I re-word this as, can there be a charge at
a place where it feels no electric force?
• Is this the same question?
Discussion question: What direction would the net
electric field be at point P at the corner of a square
which has an e- at the opposite corner and a proton
at the other two corners?
a
P
d
+
b
+
c
-e
e. The net electric field is zero
Discussion question: What direction would the
force on an electron be if it is placed at the corner
of a square which has an e- at the opposite corner
and a proton at the other two corners?
a
-e
d
+
b
+
c
-e
e. The net force is zero
Electric Field
• The direction of the Electric field is the
direction of the force on a positive test
charge at a given point.
• Radially out of a positive point charge.
• Radially into a negative point charge.
Individual question: A free proton is at a point P in
an electric field and experiences a force directed to
the right. If the proton is replaced with an electron
the electric field at this point
1. Has the same
magnitude but changes
direction
2. Increases in magnitude
and changes direction
3. Remains the same
4. Decreases in
magnitude and
changes direction.
A charge in an
electric field does
not affect the
electric field that it
(the charge) feels.
The electron will feel
a force in the
opposite direction.
Discussion question: Two charges, +Q and –Q, are
located two meters apart and there is a point along
the line that is equidistant from the two charges as
indicated. Which vector best represents the
direction of the electric field at that point?
1.
2.
3.
4.
Vector EA
Vector EB
Vector Ec
The electric
field at that
point is zero.
5. The electric
field is
opposite to EB
EB
EC
+Q
EA
-Q
Individual question: Two charges, +Q and +Q, are
located two meters apart and there is a point along
the line that is equidistant from the two charges as
indicated. Which vector best represents the
direction of the electric field at that point?
1.
2.
3.
4.
Vector EA
Vector EB
Vector Ec
The electric
field at that
point is zero.
5. The electric
field is
opposite to EB
EB
EC
+Q
EA
+Q
Individual question: Two charges, -Q and -Q, are
located two meters apart and there is a point along
the line that is equidistant from the two charges as
indicated. Which vector best represents the
direction of the electric field at that point?
1.
2.
3.
4.
Vector EA
Vector EB
Vector Ec
The electric
field at that
point is zero.
5. The electric
field is
opposite to EB
EB
EC
-Q
EA
-Q
Work out problem: A charge of +2 C is at the
origin. What charge must be placed at 2 m along
the positive x axis, to make the electric field at 2 m
along the negative x axis become zero.
1.
2.
3.
4.
5.
+4C
-4C
+8C
-8C
-2C
E=0
+2C
Q
X
2m
2m
 kq1
E1  2 rˆ
r
What is the Electric field a distance
r away from a line of charge?
 kq1
E1  2 rˆ
r
What direction is the E-field?
36 
36

kqn
Etotal   En   2 rˆ
n 1
n 1 rn

Etotal  
kdq
rˆ
2
2
x a


x2  a2
a
x
++++++++++++++++++++++++++++++++++++
dq
L
L

2
Etotal   L

rˆ 
2
kdq
ˆ
r
2
2
a x


 xiˆ  aˆj
a
2
x
2

Q dq
 
L dx
L

2
Etotal   L

2
a
kdx
2
x
2

3
( xiˆ  ayˆ )
2
Answers
•
•
•
•
•
•
•
•
•
2-b
4-b
7-a
8-c
11-3
12-1
13-2
14-5
15-4