Physics 102: Lecture 02
Coulomb’s Law
and Electric Fields
Today we will …
• get some practice using Coulomb’s Law
• learn the concept of an Electric Field
Physics 102: Lecture 2, Slide 1
Recall Coulomb’s Law
Force between charges q1 and q2 separated
distance r:
1 2
2
“Coulomb constant”
9
Opposite charges attract, like charges repel
Physics 102: Lecture 2, Slide 2
109
2
/
2
Coulomb Law practice:
Three Charges
• Calculate force on +2μC charge due to other two charges
Draw forces
Calculate force from +7μC charge
Calculate force from –7μC
7μC charge
Add (VECTORS!)
F+7
Q=+2.0μC
4m
–
–
–
–
Q=+7.0μC
Physics 102: Lecture 2, Slide 3
6m
F-7
Q=-7.0 μC
Three Charges – Calculate forces
• Calculate force on +2μC charge due to other two charges
–
–
–
–
Draw forces
Calculate force from +7μC charge
Calculate force from –7μC
7μC charge
Add (VECTORS!)
F+7
Q=+2.0μC
4m
• Calculate magnitudes
Q=+7 0μC
Q=+7.0μC
Physics 102: Lecture 2, Slide 4
6m
F-7
Q= 7 0 μC
Q=-7.0
Three charges – Adding Vectors F+7+F
F-77
• Calculate components of vectors F+7 and F-7:
F+7
4m
Q=+2.0μC
Q=+7.0μC
Physics 102: Lecture 2, Slide 5
6m
F-7
Q=-7.0 μC
Three charges – Adding Vectors F+7+F
F-77
• Add like components of vectors F+7 and F-7:
F+7
Q=+2.0μC
4m
• Final vector F has magnitude
andd direction
di ti
Q=+7.0μC
• Double-check with drawing
Physics 102: Lecture 2, Slide 6
6m
F
F-7
Q=-7.0 μC
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
Qp=1.6x10-19 C
+
r = 1x10-10 m
E
E = (9×109)(1.6×10-19)/(10-10)2 N = 1.4×1011 N/C (to the right)
Physics 102: Lecture 2, Slide 7
CheckPoint 2.1
What is the direction of the electric field at point A?
7%
1) Up
7%
2) Down
2%
3)) Left
53% 4) Right
32% 5) Zero
Physics 102: Lecture 2, Slide 8
y
A
B
x
ACT: E Field
What is the direction of the electric field at point C?
A.. Left
e
B. Right
C Zero
C.
Away from positive charge (right)
Towards negative charge (right)
Net E field is to right.
right
A
y
C
B
x
Physics 102: Lecture 2, Slide 9
E Field from 2 Charges
• Calculate electric field at point A due to two unequal charges
–
–
–
–
Draw electric fields
Calculate E from +7μC charge
Calculate E from –3.5μC
μ charge
g
Add (VECTORS!)
A
4m
Note: this is similar to ((but a bit
harder than) my earlier example.
We ll do some of this
We’ll
here… you try the rest at
home!
Physics 102: Lecture 2, Slide 10
Q = +7.0μC
6m
Q = –3.5 μC
E Field from 2 Charges
• Calculate electric field at ppoint A due to charges
g
– Calculate E from +7μC charge
– Calculate E from –3.5μC charge
– Add*
E7
E = k q/r2
A
4m
E3
Q=+7.0μC
Physics 102: Lecture 2, Slide 11
6m
Q=-3.5 μC
Adding Vectors E7+E3
• Decompose into x and y components.
components
E7
4m
E7y=E7 (4/5)
( / )
A θ
E7x=E7 (3/5)
θ
Q=+7.0μC
Physics 102: Lecture 2, Slide 12
6m
Q=-3.5 μC
Adding Vectors E7+E3
• Decompose into x and y components.
• Add components.
E7
Etotal
4m
A
Ex = 2.25×10+3 N/C
Ey = 1.0×10
1 0×10+3 N/C
Physics 102: Lecture 2, Slide 13
Q=+7.0μC
6m
E3
Q=-3.5 μC
Comparison:
Electric
l i Force vs. Electric
l i Field
ld
• Electric Force (F) – the force felt by a 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,
vectors with magnitude and direction.
direction
Ok, what is E actually good for?
Physics 102: Lecture 2, Slide 14
Electric Field Map
• Electric field defined at any location
y
A
C
B
x
Physics 102: Lecture 2, Slide 15
Electric fields:
A useful record-keeping tool!
Calculate once for fixed charges,
use to find force on other charges
(like ions/electrons in neurons,
heart tissue,
tiss e and cell membranes)
Eisenberg, BU
Physics 102: Lecture 2, Slide 16
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 –)
Physics 102: Lecture 2, Slide 17
This is becoming a mess!!!
CheckPoint 3.1
X
A
Charge A is
Y
B
Field lines start on positive charge, end on negative.
1) positive
93%
Physics 102: Lecture 2, Slide 18
2) negative
4%
3) unknown
3%
CheckPoint 3.2 / ACT
X
X
A
A
Y
Y
B
B
Compare the ratio of charges QA/ QB # lines proportional to Q
A) QA= 0.5QB
15%
Physics 102: Lecture 2, Slide 19
B) QA= QB
17%
C) QA= 2 QB
53%
CheckPoint 3.4
X
A
Y
B
The electric field is stronger when the
lines are located closer to one another.
The magnitude of the electric field at point X is greater than at point Y
1) True
18%
Physics 102: Lecture 2, Slide 20
2) False
82%
Density of field lines gives E
E inside of conductor
• Conductor ≡ electrons free to move
– El
Electrons feels
f l electric
l i force
f
- will
ill move until
il
they feel no more force (F=0)
– F=Eq:
F E if F
F=0
0 th
then E
E=00
• E=0 inside a conductor (Always!)
Physics 102: Lecture 2, Slide 21
Demo: E-field
E field from dipole
y
A
C
B
x
Physics 102: Lecture 2, Slide 22
Recap
• E Field has magnitude and direction:
– E ≡ F/q
– Calculate jjust 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
• Campus closed on Monday; no office hours.
• Homework 1 due Wednesday, Jan 23 @ 8 AM!
• Do your Checkpoint by 8:00 AM Wednesday.
Physics 102: Lecture 2, Slide 24