Electric Fields

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Electric Fields

• By Tuhin Chatterjee
• and HyeYun Park

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Background on Electric Fields
Electric Dipole Field
Electric field lines always begin on a positive
charge and end on a negative charge and do not
start or stop in midspace. The number of field
lines leaving a positive charge or entering a
negative charge is proportional to the magnitude
of the charge.
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Magnetic Force

• Lorentz Force Law

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Gauss' Law
The net flux through any closed surface is
proportional to the net charge enclosed by that
surface, i.e., Eda ? þdv
Surface Volume
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Point Electrode
Point charge limit of an infinite charge
density occupying zero volume 8.854 x
10-12 farad/meter, permitivity of free
space Using Gauss Law As x x E Qtotal E
Qtotal / ( x As) Lets Area 4p(r2) E
Qtotal / 4p (r2)
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Infinity Planar Electrode
s, Charge per unit area on the plane (SI C/m 2)
Qtotal/Area

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Electric Field with thin Passive layer
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Two infinite planar

• UPPER SIDE
• ?E ds ? E ds ? Eds Q(r)As/
• AsE(r) AsE(r) 0 Q(r)As/
• E(r) Q(r)/2
• LOWER SIDE
• E(r)- - Q(r)/2
• Total Electric Field
• ? E(r)-E(r)- Q(r)/

Bottom Top Side
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Two Finite Planar
Parallel Plate Capacitor
Charge density s q/A E q/(e0A) s/e0
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Example

• An electron enters the region of a uniform
  electric field as in the figure, with v0 3.00
  106 m/s and E 200 N/C. The width of the plates
  is l 0.100 m.
• (e 1.60 10-19 C and me 9.11 10-31 kg)
• Find the acceleration of the electron while in
  the electric field.
• Find the time it takes the electron to travel
  through the region of the electric field.
• What is the vertical displacement y of the
  electron while it is in the electric field?
• Find the speed of the electron as it emerges from
  the electric field.

Solution
a 3.51 1013 m/s2, t 3.33 10-8 s, y -1.95
cm, v 3.22 106 m/s
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Cylindrical Electrode

• ?E ds ? E ds ? Eds Q(r)/
• 0 2prhE(r) 0 Q(r)/
• 2prhE(r) Q(r)/
• E(r) Q(r)/(2prh )

Bottom Side
Top
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Dome Shape Electrode

• r gtR
• ?E ds Q(r)/
• (4pr2/2) x E(r) Q(r)/
• E(r) Q(r)/(2pr2 )
• rltR
• E(r) 0

Surface
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USEFUL EQUATION
(rho) for the charge per unit volume, the volume
density (sigma) for the charge per unit area, the
area density (lambda) for the charge per unit
length, the linear density  
Thus we can write   Cm-3, Cm-2, Cm-1.
Gauss Law The net flux through any closed
surface is proportional to the net charge
enclosed by that surface, i.e.,