Download Electrostatics

Electrostatics
Chapter 21-24
Properties of Physical Objects
• Mass/Inertial:
– Gravity mass: inertia in gravitational interaction
– Kinetic mass: inertia in any motion
• Charge
– Origin of charge: charged microscopic particles,
electron, proton, neutron
– Interaction between charges
• Spin
– Properties involved in magnetic interaction
– Microscopic origin: particles, electron, proton,
neutron, etc.
Charge
• Smallest charge unit: charge of 1 electron
– 1 electron = 1.602x10-19Coulomb
• Conservation of net charge
– The number of positive and negative can change
• Creation of charged objects
– Two objects rubbed together
– Charging by induction
– Charging by conduction
Point Charge Model
Charge-Charge interaction
• Description
– Point model ( spatial distribution description)
– Charged point ( physical property of the point)
– Extensible (continuous distribution can be built based on
many points model)
• Interaction
– Point-to-point electrotatic interaction (Coulomb’s Law)

kq1q2
F12  2 r̂12
r12
– Superposition
for many points model
 principles

Fi   Fji
j i
Examples
Electrostatic Interaction
• Conservation
 
i  Fi  0
– There exists a potentialenergy function Ui

U (ri )  Fi
– Potential energy function is not unique
• Can differ by a constant: U+c is also valid
• Commonly used: U(r=∞)=0; U(r) = kq1q2/r
– Potential: due to distribution of other charges
 kq j 

 
U (ri )  qi 
  qi   (ri ; rj i ; q j i )
 j i rji 
Examples
Electric Field
• Need to introduce electric field: Separating intrinsic
and extrinsic factors
– Consider many point charges model


  
 kq j 
Fi   F ji  qi  2 rˆji   qi  E (ri ; rj i ; q j i )
 j i rji 
j i
– Electrostatic Force of ith point charge is equal to
charge qi (properties of the point: intrinsic) times a
function E (property related to space and properties
of other point charges: extrinsic)
– Function E is called electric field which is a vector
quantity at a space location due to charges
Properties of Electric Field
• Distribution of vector E forms a vector field
 
 
– Curl of Electric Field:   F 0   E  0
– Divergence of Electric Field:   E   /  0
– Electron density ρ
• Representation of Electric Field
– Line representation of vector field:
• No cross-over (curl of electric field = 0)
• Originate from positive charge/End at negative charge
• Intensity proportional to line density
Examples
• Electric field due to point charge
+
+
-
• Simplest electric field 

– Uniform electric field:
Q
-Q
+

E r   E
+
Electric Flux and Gauss’s Law 
• Flux ΦE is a concept for vector field.
– In the line representation: flux is the
number of field lines crossing over a given
surface
– Since the field line density is proportional
to electric field, the number of field lines
should be electric field integrate over the
surface
 
 
 E   E  dA   E  ndA
• Gauss’s Law for Enclosed Surface
– ΦE of enclosed surface = charge enclosed
divides free space permitivity
 
 
q
 E   E  dA   E  n dA 
0
f

dA  dA  nˆ
dA
S
Simple Charge Distribution Models
If the charge is distributed over a volume, surface or a line, we
can relate the geometrical size of the object with the charge.
+
+
+
+
dV
+
dl
dQ =  · dl
dA
+
+
+
+
+
+
+
+
+
+
+
+
+
+
dQ =  · dA
linear charge density
+
+
++
+
++
+
+
+
++
+
+
+
++
+
+
+
+
+
dQ =  · dV
surface charge density
volume charge density
Examples