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Protons and electron carry charge
Presence of charge creates an electric field
The field creates potential differences
between points within the space it exists
Other charges react to this field and potential
and move about (current)
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Charge is carried by electrons
and protons.
Can be positive or negative.
Like charges repel, opposite
charges attract.
Total charge in a system is
conserved.
Charges come in discrete
quantities.
Charges are measured in
Coulombs (C).
Usually denoted by q.
q1
q2
r

q1q2
F12  ke 2 rˆ
r
ke 

 Fe
q
E
 ke 2 rˆ
q0
r
1
4 0
 8.99  109 N.m2 C2
 0  8.85  1012 C2 N.m2
E-Field
Force
Acceleration

E


F  qE


 F qE
a 
m m
A way to visualize field
patterns over space.
 The e-field is tangent
to the field lines at
each point and along
the direction of the
field arrow.
 The density of the lines
is proportional to the
magnitude of the efield.
 Field lines start from
positive charges an
end at negative ones.
 Field lines can not
cross.

Electric Flux
Gauss’ Law
 
 E   E.dA
surface
  qin
 E   E.dA 
0
Q
E  ke 2
r
Q
E  ke  3  r
a 
r>a
r<R

E
2 0
E

2 0 r
The electric field is zero everywhere
inside a conductor at electrostatic
equilibrium.
 Any net charge on a conductor will
reside on the surface.
 The electric field just outside a
conductor is perpendicular to the
surface and is proportional to the
charge density.
 The charge density is highest near
parts of the conductor with the
smallest radius of curvature.


E
0
 
U  q0  E.d s
B
Electric Potential Energy
A
 
U
V 
   E.d s
q0
A
B
Potential Difference
In a Uniform Field
For a Point Charge
For a Charge Distribution
V   Ed
q
V  ke
r
dq
V  ke 
r
V
Ex 
x
V
Ey 
y
V
Ez 
z
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Charges always reside at
the outer surface of the
conductor.
The field lines are always
perpendicular to surface.
Then E.ds=0 on the surface
at any point.
Which means, VB-VA=0
along the surface.
The surface is an
equipotential surface.
Finally, since E=0 inside the
conductor, the potential V is
constant and equal to the
surface value.
Q
C
V
Parallel Plate
Capacitor
For series
capacitors
For parallel
capacitors
Q 0 A
C

V
d
n
1
1

Ceq j 1 C j
n
Ceq   C j
j 1
(C/V=F)
Stored Energy in a Capacitor
Q2 1
1
U
 QV  C (V ) 2
2C 2
2
Capacitor with a dielectric
C  C0
dQ
I (t ) 
dt
J  E
V
R
I
1
l

R

A
R  R0 1   T  T0 
2



V
P  IV  I 2 R 
R
Series Req 
R
i
i
Parallel
1
1

Req
i Ri
I
Kirchoff’s
Rules
in
junction
RC Circuits

I
out
junction
 V  0
closed
loop

 
q(t )  CE 1  et RC  Q 1  et RC
I (t ) 
dq E t RC
 e
dt R
q(t )  Qet RC
I (t ) 
dq
Q t RC

e
dt
RC
