Physics 2113
Jonathan Dowling
Physics 2113
Lecture 05: WED 02 SEP
Electric Fields I
Charles-Augustin
de Coulomb
(1736-1806)
What Are We Going to Learn?
A Road Map
•  Electric charge
- Electric force on other electric charges
- Electric field, and electric potential
•  Moving electric charges : current
•  Electronic circuit components: batteries, resistors,
capacitors
•  Electric currents - Magnetic field
- Magnetic force on moving charges
•  Time-varying magnetic field & Electric Field
•  More circuit components: inductors.
•  Electromagnetic waves - light waves
•  Geometrical Optics (light rays).
•  Physical optics (light waves)
Coulomb’s Law
+ q1
F12
−q2
F21
r12
k | q1 | | q2 |
| F12 |=
2
r12
For Charges in a
Vacuum
k
2
N
m
9
8
.
99
×
10
=
C2
Often, we write k as:
k= 1
4πε 0
Charles-Augustin
de Coulomb
(1736-1806)
with ε 0 = 8.85 × 10
−12
2
C
N m2
Sir Michael Faraday’s Electric Lines of Force
Electric
Force Field
Faraday (1791–1867)
E-Field is E-Force Divided by E-Charge
!
! F
E=
q
Definition of
Electric Field:
!
k | q1 | | q2 |
| F12 |=
2
r12
!
k | q2 |
| E12 |=
2
r12
EForce
on
Charge
+q1
P1
P1
–q2
P2
!
E12
E-Field
at Point
Units: F = [N] = [Newton] ;
!
F12
–q2
P2
E = [N/C] = [Newton/Coulomb]
Electric Fields
•
Electric field E at some point in space
is defined as the force experienced by
an imaginary point charge of +1 C,
divided by 1 C.
•
•
•
Note that E is a VECTOR.
Electric Field of a Point Charge
Since E is the force per unit charge, it
–q
E
+1C
is measured in units of N/C.
R
We measure the electric field using
very small “test charges”, and dividing
the measured force by the magnitude
of the charge.
k |q|
| E |= 2
R
Compare to Gravitational to Electric Fields
Gravitational
Force:
(Units: Newtons = N)
GmM
F=− 2
r
Gravitational
Field:
g=−
(Units: N/kg)
GM
r2
Given the Field,
Find the Force:
F = mg
Find the Force:
(Vector Form)
r̂
!
g = −GM 2
r
!
r̂
!
F = −mg = −GmM 2
r
Electric
Force:
(Units: Newtons = N)
Electric Field:
(Units: N/C)
Given the Field,
Find the Force:
Find the Force:
(Vector Form)
kqQ
F=
r2
kQ
E= 2
r
F = qE
!
r̂
E = kQ 2
r
!
!
r̂
F = qE = kqQ 2
r
Compare to Electric Field to Gravitational Field
Gravitational
Field Lines
Electric Field
Lines
!
g
!
E
!
F
m
r̂
Note: Field Exists in
Empty Space
Whether Test Mass
m is There or Not!
!
F
+q
r̂
Note: Field Exists in
Empty Space
Whether Test
Charge +q is There
or Not!
Electric Field Lines
•  Field lines: useful way to
visualize electric field E
•  Field lines start at a positive
charge, end at negative
charge
•  E at any point in space is
tangential to field line
•  Field lines are closer where
E is stronger
Example: a negative
point charge — note
spherical symmetry
Direction of Electric Field Lines
E-Field Vectors
Point Away from
Positive Charge
— Field Source!
E-Field Vectors
Point Towards
Negative Charge
— Field Sink!
!
ESe
!
E Re
!
!
E Re + E Rp
!
!
ESp + ESe
!
E R,net
!
ES,net
ICPP
Superposition of F and E
•
Question: How do we figure out
the force or field due to several
point charges?
•
Answer: consider one charge at
a time, calculate the field (a
vector!) produced by each
charge, and then add all the
vectors! (“superposition”)
•
Useful to look out for
SYMMETRY to simplify
calculations!
•
If you never learned to add
vectors in 2101 you’ll be in
serious trouble in 2102!
See online review http://
phys.lsu.edu/~jdowling/
PHYS21024SP10/Vectors.pdf
ICPP
Total electric field
-2q
+q
•  4 charges are placed at the corners of
a square as shown.
•  What is the direction of the electric
field at the center of the square?
(a) Field is ZERO!
(b) Along +y
(c) Along +x
!
! F
E≡
+q
-q
y
+2q
+q ≡ +1.0C
+q is the test charge
x
ICPP: Which Way is Enet?
!
Enet