physics 1161 lecture 2 vectors & electric fields
DESCRIPTION
Physics 1161 Lecture 2 Vectors & Electric Fields. Three Charges. Example. Calculate force on +2 m C charge due to other two charges Calculate force from +7 m C charge Calculate force from –3.5 m C charge Add (VECTORS!). Q=+2.0 m C. 4 m. 6 m. Q=+7.0 m C. Q=-3.5 m C. Example. - PowerPoint PPT PresentationTRANSCRIPT
Physics 1161 Lecture 2Vectors
&Electric Fields
Three Charges
Q=-3.5 CQ=+7.0C
Q=+2.0C
6 m
4 m
• Calculate force on +2C charge due to other two charges– Calculate force from +7C charge
– Calculate force from –3.5C charge
– Add (VECTORS!)
6 6
1,3 22 2
7 10 2 10
3 4
k C CF
m m
35.04 10 N
35.04 10 N
6 6
2,3 22 2
3.5 10 2 10
3 4
k C CF
m m
32.52 10 N
32.52 10 N
Three Charges
Q=-3.5 CQ=+7.0C
Q=+2.0C
6 m
4 m
• Resolve each force into x and y components
• Add the x-components & the y-comp.
• Use Pyth. Theorem & Trigonometry to express in R,θ notation
3 31,3 5.04 10 cos53 3.03 10oxF N N
35.04 10 N
3 32,3 2.52 10 cos307 1.51 10oxF N N
32.52 10 N
53o
53o
3 31,3 5.04 10 sin 53 4.03 10oyF N N
3 32,3 2.52 10 sin 307 1.997 10oyF N N
3 3 33.03 10 1.51 10 4.54 10xF N N N
3 3 34.03 10 1.997 10 2.03 10yF N N N
Three Charges
• Use Pyth. Theorem & Trigonometry to express in R,θ notation
34.54 10 N
32.03 10 N
2 23 34.54 10 2.03 10F N N
34.9 10F N
φ
3
3
2.03 10arctan arctan 24
4.54 10y o
x
F N
F N
Since resultant is in first quadrant, θ = φ 24o
F
Electric Force on Electron by Proton
• What are the magnitude and direction of the force on the electron by the proton?
+
r = 1x10-10 m
q=1.6x10-19 C
Toward the left
2
2
1 22
9 19 19
210
8
9 10 1.6 10 1.6 10
10
2.30 10
N mC
kq qF
r
C CF
m
F N
e-
Comparison:Electric Force vs. Electric Field
• Electric Force (F) - the actual force felt by a charge at some location.
• Electric Field (E) - found for a location only – tells what the electric force would be if a charge were located there:
F = qE• Both are vectors, with magnitude and
direction
Electric Field
• Charged particles create electric fields. – Direction is the same as for the force that a + charge
would feel at that location.
– Magnitude given by: E F/q
• Field at A due to proton?
+
r = 1x10-10 m
q=1.6x10-19 C
Toward the right
2
2
2
9 19
210
11
9 10 1.6 10
10
1.44 10
N mC
kqE
r
CE
m
NE C
A
What is the direction of the electric field at point A, if the two positive charges have equal magnitude?
1 2 3 4 5
0% 0% 0%0%0%
1. Up2. Down3. Right4. Left5. Zero
x
yA
B+ +
What is the direction of the electric field at point A, if the two positive charges have equal magnitude?
1 2 3 4 5
0% 0% 0%0%0%
1. Up2. Down3. Right4. Left5. Zero
x
yA
B+ +
Preflight 2.2
What is the direction of the electric field at point A?
1) Up
2) Down
3) Left
4) Right
5) Zero x
yA
B+
30%
0%
0%
30%
40%
Preflight 2.3
What is the direction of the electric field at point B?
1) Left
2) Right
3) Zero
x
yA
B+
70%
30%
What is the direction of the electric field at point C?
1 2 3
0% 0%0%
1. Left2. Right3. zero
x
y
C+ -
Electric Field Applet
• http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html
A B
X
Y
Preflight 2.5
Charge A is
1) positive 2) negative 3) unknown
Field lines start on positive charge, end on negative.
80% 0% 20%
Preflight 2.6
Compare the ratio of charges QA/ QB
1) QA= 0.5QB 2) QA= QB 3) QA= 2 QB
# lines proportional to |Q|
A B
X
Y
20% 30% 40%
A B
X
Y
Preflight 2.8
The magnitude of the electric field at point X is greater than at point Y
1) True 2) False Density of field lines gives E
The electric field is stronger when the lines are located closer to one another.
10% 90%
Compare the magnitude of the electric field at point A and B
0%0%0%
1 2 3
A
B
1. EA> EB
2. EA= EB
3. EA< EB
Physics 1161: Lecture 2, Slide 18
E inside of conductor• Conductor electrons free to move– Electrons feels electric force - will move until
they feel no more force (F=0)– F=qE: if F=0 then E=0
• E=0 inside a conductor (Always!)
Physics 1161: Lecture 2, Slide 19
E inside of conductor
• Conductor electrons free to move– Electrons feel electric force - will move until
they feel no more force (F=0)– F=qE: if F=0 then E=0
• E=0 inside a conductor (Always!)
A B
X
Y
Preflight 2.10
"Charge A" is actually a small, charged metal ball (a conductor). The magnitude of the electric field inside the ball is:
(1) Negative (2) Zero (3) Positive40% 10% 50%
Physics 1161: Lecture 2, Slide 21
Recap
• E Field has magnitude and direction:– EF/q– Calculate just like Coulomb’s law– Careful when adding vectors
• Electric Field Lines– Density gives strength (# proportional to charge.)– Arrow gives direction (Start + end on -)
• Conductors– Electrons free to move E=0