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Physics 102: Lecture 2, Slide 1
Coulomb’s Lawand Electric Fields
Physics 102: Lecture 02
Today we will … • get some practice using Coulomb’s Law• learn the concept of an Electric Field
Physics 102: Lecture 2, Slide 2
Recall Coulomb’s Law• Magnitude of the force between charges q1 and q2
separated a distance r:F = k q1q2/r2 k = 9x109 Nm2/C2
• Force is – attractive if q1 and q2 have opposite sign
– repulsive if q1 and q2 have same sign
• Units:– q’s have units of Coulombs (C)
• charge on proton is 1.6 x 10-19 C
– r has units of m
– F has units of N
Physics 102: Lecture 2, Slide 3
Coulomb Law practice: Three Charges
Q=-7.0 C
Q=+2.0C
6 m
4 m
• Calculate force on +2C charge due to other two charges– Draw forces
– Calculate force from +7C charge
– Calculate force from –7C charge
– Add (VECTORS!)
1
2
3
4
5
6
7
8
9
10
11
1
2
F+7
Q=+7.0C
F-7
Physics 102: Lecture 2, Slide 4
Three Charges – Calculate forces
Q=-7.0 C
Q=+2.0C
6 m
4 m
• Calculate force on +2C charge due to other two charges– Draw forces
– Calculate force from +7C charge
– Calculate force from –7C charge
– Add (VECTORS!)
• Calculate magnitudes
F+7
Q=+7.0C
F-7
𝐹= 𝑘𝑞1𝑞2𝑟2
Physics 102: Lecture 2, Slide 5
Q=-7.0 C
Q=+2.0C
6 m
4 m
F+7
Q=+7.0C
F-75 m
Three charges – Adding Vectors F+7+F-7
• Calculate components of vectors F+7 and F-7:
𝐹+7,𝑥 = 𝐹+7 cos𝜃 = 5× 10−3𝑁35
𝐹−7,𝑥 = 𝐹−7 cos𝜃 = 5× 10−3𝑁35
𝐹+7,𝑦 = 𝐹+7 sin𝜃 = 5× 10−3𝑁45
𝐹−7,𝑦 = −𝐹−7 sin𝜃 = −5× 10−3𝑁45
Physics 102: Lecture 2, Slide 6
Q=-7.0 C
Q=+2.0C
6 m
4 m
F+7
Q=+7.0C
F-75 m
Three charges – Adding Vectors F+7+F-7
• Add like components of vectors F+7 and F-7:
F
𝐹𝑥 = 𝐹+7,𝑥 + 𝐹−7,𝑥 = 6× 10−3𝑁 𝐹𝑦 = 𝐹+7,𝑦 + 𝐹−7,𝑦 = 0
𝐹=ට𝐹𝑥2 + 𝐹𝑦2 = 6× 10−3𝑁
𝜑 = tan−1 𝐹𝑦𝐹𝑥 = 0
• Final vector F has magnitude and direction
• Double-check with drawing
Physics 102: Lecture 2, Slide 7
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 = kq/r2
+
r = 1x10-10 m
Qp=1.6x10-19 C
E
E = (9109)(1.610-19)/(10-10)2 N = 1.41011 N/C (to the right)
Physics 102: Lecture 2, Slide 8
Preflight 2.3What is the direction of the electric field at point B?
1) Left
2) Right
3) Zero
x
yA
B
Physics 102: Lecture 2, Slide 9
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
Physics 102: Lecture 2, Slide 10
ACT: E FieldWhat is the direction of the electric field at point C?
A. Left
B. Right
C. Zero
x
y
C
A
B
Physics 102: Lecture 2, Slide 11
E Field from 2 Charges
Q = –3.5 C
A
6 m
4 m
• Calculate electric field at point A due to two unequal charges– Draw electric fields
– Calculate E from +7C charge
– Calculate E from –3.5C charge
– Add (VECTORS!)
Note: this is similar to (but a bitharder than) my earlier example.
Q = +7.0C
Physics 102: Lecture 2, Slide 12
Comparison:Electric Force vs. Electric Field
• Electric Force (F) – the actual force felt by a real charge at some location
• Electric Field (E) – found for a location only (any location) – tells what the electric force would be if a charge were located there:
F = Eq• Both are vectors, with magnitude and direction.
Physics 102: Lecture 2, Slide 13
x
y
C
A
B
• Electric field defined at any location (we did three: A, B, C)
Electric Field Map
Physics 102: Lecture 2, Slide 14
-5 -4 -3 -2 -1 0 1 2 3 4 5-5
-4
-3
-2
-1
0
1
2
3
4
5
-6 -4 -2 0 2 4 6-6
-4
-2
0
2
4
6
Electric Field Lines• Closeness of lines shows field strength (lines never cross)• Number of lines at surface Q• Arrow gives direction of E (Start on +, end on –)
This is becoming a mess!!!
Physics 102: Lecture 2, Slide 15
A B
X
Y
Preflight 2.5
Charge A is
1) positive 2) negative 3) unknown
Physics 102: Lecture 2, Slide 16
A B
X
Y
Preflight 2.6
Compare the ratio of charges QA/ QB
1) QA= 0.5QB 2) QA= QB 3) QA= 2 QB
A B
X
Y
Physics 102: Lecture 2, Slide 17
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
Physics 102: Lecture 2, Slide 18
ACT: E Field Lines
Compare the magnitude of the electric field at point A and B
1) EA>EB 2) EA=EB 3) EA<EB
A
B
Physics 102: Lecture 2, Slide 19
E inside of conductor• Conductor electrons free to move
– Electrons feels electric force - will move until they feel no more force (F=0)
– F=Eq: if F=0 then E=0
• E=0 inside a conductor (Always!)
Physics 102: Lecture 2, Slide 20
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) Positive
Physics 102: Lecture 2, Slide 21
Demo: E-field from dipole
x
y
C
A
B
Physics 102: Lecture 2, Slide 22
Recap• E Field has magnitude and direction:
– E F/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
Physics 102: Lecture 2, Slide 23
To Do
• Do your preflight by 6:00 AM Wednesday.