Transcript Lecture 1 Electricity

普通物理學甲下 (202 101A2)
General Physics(A)(2)
台大物理 吳俊輝

Lectures:
 每週三、五, 第3、4節 (10:20~12:10), Feb.18 ~ Jun.19, 2009
 April 3 (Friday) 溫書假, May 29 (Friday) 彈性放假

Exams:
 期中考：April 15/17 (10:20~12:10), 2009
 期末考：June 17/19 (10:20~12:10), 2009
Electricity I
Coulomb’s Law
 Static
electricity is analogous to
gravity.
 It was found that “charges” can
attract or repel each other
according to a force law –
Coulomb’s Law.
 SI unit of charge is coulomb (C)
 0 is the permittivity constant.
F
1
q1 q2
1
4 0
r2
4 0
 8.85 1012 C 2 /( N  m 2 )
Some properties of electric charges

Charge is quantized in the units of e, the electric
charge ( n  1, 2, 3,... ).
q  ne
e  1.602 1019 C

Charge is conserved (in a reaction)
In PET, we saw the annihilation reaction
e  e    
There is also a reaction called the pair
production in which a photon is converted into
an electron-positron pair
  e  e
The concept of a field


In static electricity, it is useful
to figure out the electric
effect of a charge distribution,
so the concept of an electric
field is introduced.
Basically, an electric field is
defined to be the force acting
on a small + test charge q0
when the test charge is
placed near another charge
distribution.
F
E
q0
Electric field of a point charge
In the case of a point
charge, we know from
Coulomb’s Law that
1 q q0
F
4 0 r 2
 And the magnitude of
the electric field is

E

1
q
4 0 r 2
Directions?
F
1
q q0
4 0
r2
Electric field examples – a pairs of +
charges and a pair of + and - charge
Electric field example – large
charged conducting plane

The electric field generated by a large + charged
conducting plate is perpendicular and directed
away from the conducting plane.
Electric field and ink jet printer

Operational principles of an ink jet printer:
1. Generator G shoot out ink drops.
2. Charging unit C charges the ink drops to different levels.
3. The electric field of the deflecting plates then direct the
ink drops to a position on the paper that depends on the
amount of charge on the ink drops.
Electric dipole –a very important example

Consider a pair of + and –
charges separated by a
distance d.
E  E(  )  E(  )
q  1
1 
E
 2  2 
4 0  r(  ) r(  ) 
2
2

d 
d  

E
1
  1 
 
2 
4 0 z 
2z 
2 z  

q
E
 d
qd
  d

1


...

1


...


 

3
4 0 z 2 
z
z
 
  2 0 z
q
E  E(  )  E(  )
Electric dipole moment

So we can define
E

p
2 0 z 3
p is the electric dipole moment
with magnitude given by
p  qd
and it is a vector pointing from –
to + charge.
Molecular dipole



An electric dipole is a very
important model because it is the
“simplest” way to describe charge
distribution in a system.
For example, in a water molecule,
there is a net electric dipole
moment pointing away from the
oxygen atom toward the hydrogen
atoms.
When we get to quantum mechanics,
we will see that the interaction of a
molecule with photons require the
use of electric dipole.
Electric dipole


Suppose we have the
given charge
distribution. Although
it looks complicated,
we know that the sum
of all electric dipoles
will give rise to a net
electric dipole that
points somewhat
towards the right.
So the electric dipole
is an easy and
convenient way for us
to understand the
electric properties of
a charge distribution.









Net electric dipole

Electric dipole in an external E field

The torque on the dipole:
  Fx sin   F (d  x) sin   Fd sin 
p  qd ,   pE sin 
  p E

Basically the torque will
rotate the electric dipole until
it is aligned with the E field
such that
  p E  0
x



Associated with the torque is a Potential Energy (U).
Define U  0 when p  E (  90)
U at a given  is the external work (Wext) required to
rotate the electric dipole from 90 degrees to  (which
equals the negative of the work WE done by the E
field):
U   WE


90

90
 Wext

90

   ext d
90
pE sin  d   pE cos 

U  pE