Review
Coulomb’s Law
Q1Q2
F k 2
r
Units of Charge
1 Coulomb (C)
k  8.988 10 N  m / C  9.0 10 N  m / C
9
2
2
9
2
2
Direction of the electric force is always along
the line joining the two objects.
Direction of the force depends on whether the
charges have the same sign or opposite sign.
Coulomb’s Law in terms of e0,
permittivity of free space.
1 Q1Q2
F
;
2
4e 0 r
1
12 2
2
e0 
 8.85  10 C / N  m .
4k
Conceptual Example
Two positive point charges Q1=50 mC and Q2=1 mC, are
separated by a distance l. Which is larger in magnitude, the force
that exerts on Q1 exerts on Q2, or the force that Q2 exerts on Q1?
The Electric Field
The electric field E at a point in space is
defined as an electric force F, acting on a
positive test charge q divided by the
magnitude of the test charge

 F
E
q
1
Q
E
2
4e 0 r
Units of Electric Field
1 N/C
Field Lines
1. At every point of electric field line,
electric field E is tangent to this line. No
two field lines can cross!
2. The line must begin at positive charge and
terminate on the negative one unless go to
infinity.
3. The number of line per unit area is
proportional to the magnitude of electric
field.
Electric Fields and Conductors
Important: electric field inside of good
conductor is zero!!!!
Important: any net charge on a good
conductor distributes itself on the
surface!!!!
Electric field is always perpendicular to the surface of
conductor:
P
d
q
d
Q
Is it possible to place a charge at point Q such
that the electric field produced at point P by
the two charges will be add to zero?
Electric Potential and Electric
Energy
It’s useful to define the electric potential (or
simply the potential) as a potential energy per
unit charge:
PEa
Va 
q
Units of Electric Potential
1 V = 1 J/C
Vba
E
d
Important: this simple formula for E
may be used only for uniform field!!!!
Equipotential Lines
The equipotential surface must be perpendicular to the surface.
Important: the surface of a good
conductor is always an equipotential
surface!!!!
Electric Potential Due to Point
Charges
1 Q
V
4e 0 r
Work to Force Two Positive
Charges Close Together
What minimum work is required by an external force to
bring a charge q=3.00 mC from a great distance away to a
point 0.5 m from a charge Q=20mC?
Capacitance
Q = CV
The constant of proportionality, C ,
in the last relation is called the
capacitance of the capacitor.
Important: the capacitance C is a
constant for a given capacitor; it
does not depend on charge Q or
voltage V.
Capacitance of a Parallel-Plate
Capacitor
A
C  e0
d
A
C  Ke 0
d
Energy Stored in Capacitor
2
1
1
1Q
2
U  QV  CV 
2
2
2 C
When such a circuit is formed, charge can flow through
the wires of the circuit, from one terminal of the battery to
the other. A flow of charge such as this is called as electric
current.
Q
I
t
Units of Current
1 Ampere (A) = 1 C /1 s
Important: Current is not a vector, it’s a
scalar!!!!
Definition of Resistance
I=V/R
Ohm’s Law
The current through a metal conductor is
proportional to the applied voltage.
Resistivity
L
R
A
Effect of Temperature
T  0 (1   (T  T0 ))
 – temperature coefficient of
resistivity is positive for metals
and negative for semiconductors.
Electric Power
2
V
P  IV  I R 
R
2
V  V0 sin 2ft
V V0
I   sin 2ft
R R
2
2
2
P  I R  I 0 R sin 2ft
Average Power
1 2
P  I0 R
2
2
1 V0
P
2 R
Root-Mean-Square Values (RMS)
I rms
Vrms
I0
 I 
 0.707 I 0
2
V0
2
 V 
 0.707V0
2
2