Electrostatics
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Transcript 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)
kq 1 q 2
F12
rˆ12
2
r12
– Superposition
for many points model
principles
Fi
F
ji
ji
Examples
Electrostatic Interaction
• Conservation
i Fi 0
– There exists a potentialenergy function Ui
U ( ri ) F i
– 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 ) q i
q i ( ri ; r j i ; q j i )
j i r ji
Examples
Electric Field
• Need to introduce electric field: Separating intrinsic
and extrinsic factors
– Consider many point charges model
Fi
ji
kq j
F ji q i 2 rˆ ji q i E ( ri ; r j i ; q j i )
j i r ji
– 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
F 0 E 0
– Curl of Electric Field:
– 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
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• Simplest electric field
– Uniform electric field: E r E
Q
-Q
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+
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 d A E n dA
• Gauss’s Law for Enclosed Surface
– ΦE of enclosed surface = charge enclosed
divides free space permitivity
q
E E d A E n dA
0
d A dA nˆ
f
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.
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dV
+
dl
dQ = · dl
dA
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dQ = · dA
linear charge density
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dQ = · dV
surface charge density
volume charge density
Examples