Experimental Physics EP2a
Electricity and Wave Optics
– Electric charge –
Conductors, Coulomb’s law
Rustem Valiullin
http://research.uni-leipzig.de/valiu/
Experimental Physics IIa - Electric charge, field, dipole
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Air
Human Hands
Asbestos
+
Glass
Electric charge
+
-
-
-
+
+
Human Hair
Mica
Nylon
Wool
Lead
Silk
Aluminum
Paper
Cotton
Benjamin Franklin
January 17, 1706 Boston
April 17, 1790 Philadelphia
-e
Steel
Wood
Rubber balloon
e = 1.602177  10-19 C
Hard rubber
+e
Nickel, Copper
Brass, Silver
Charge is conserved.
Gold, Platinum
Sulfur
Celluloid
Silicon
Teflon
Experimental Physics IIa - Electric charge, field, dipole
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Coulomb’s law
The force exerted between two charges acts along the
line connecting the charges.
It varies inversely proportional to the square of the
distance separating the charges.
It is proportional to the product of the charges.
The force is repulsive if the charges have the same sign
and attractive if they are opposite.

kq1q2
F1, 2  2 r̂1, 2
r1, 2
k q1q2
F1, 2  2
r1, 2
1

r1, 2
2
k  8.9875  109 N  m2 /C2
k  4 0 
1
Experimental Physics IIa - Electric charge, field, dipole
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Some examples
e = 1.6  10-19 C
mp = 1.67  10-27 kg
me = 9.11  10-31 kg
G = 6.67  10-11 N m2 kg-2
q1  1 nC
Fe
?
Fg
r  5.3  1011 m
Fe  ?
q1  1 nC
a ?
q1  2 nC
Experimental Physics IIa - Electric charge, field, dipole
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To remember!
 Unlike charges attract one another, like charges repel.
 Charge is conserved.
 Charge is quantized – integer number of electronic charge.
 Conductors are materials in which electrons move freely.
 In insulator electrons do not move freely.
 Coulomb’s law states that force due to charges:
(i) inversely proportional to square distance,
(ii) proportional to the product of charges,
(iii) the proportionality constant is called
the Coulomb constant.
Experimental Physics IIa - Electric charge, field, dipole
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Electric field

F
-
F3
•q0 is a test charge
(i.e. q0 is small enough
F2
q
+ 0
to not alter the electric field)
• q0 is positive
+
E  lim F / q0
q0  0
F1
-
F  F1  F 2  F 3
1 N / C  1 kg  m  s 3  A1  1V
Experimental Physics IIa - Electric charge, field, dipole
/m
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Electric field
Coulombs law:

ri , P
electric field, due to charge qi at point P
E i,P
kqi
 2 rˆi , P
ri , P
-q
i
E i,P
P
net electric field, due to a distribution of point charges
E P   E i,P
i
kqi
  2 rˆi , P
i ri , P
Experimental Physics IIa - Electric charge, field, dipole
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Electric field lines
electric field lines (also lines of force) show the
direction of the force exerted on a positive test
charge
electric field lines begin on positive charges (or
infinity) and end on negative charges (or
infinity)
+
the electric field lines point radially away from
positive charges and towards negative
charges
the density (spacing) of the lines is
proportional to the electric field strenght at
that point
the number of lines leaving or entering a
charge is proportional to the magnitude of the
charge
field lines do not cross
Experimental Physics IIa - Electric charge, field, dipole
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Electric field lines
monopole
equal charges, but
2 equal
different
charges
magnitude)
opposite charges
2 opposite
with different
chargesmagnitudes
Experimental Physics IIa - Electric charge, field, dipole
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Motion of a Point Charge in the Electric Field

a
F  q E
m
the rest is mechanics…
m
example: electron in uniform electric field
How far can it travel until it is momentarily stopped?
E
Ex  1kN / C
v0, x  2 106 m / s
-
Fx  eE
ax 

m
m
v x v
2
x 
2
0, x
2a x

v0
e
vx  0
x 
mv02, x
Experimental Physics IIa - Electric charge, field, dipole
2eE
 1.14cm
10
Motion of point-like charges in electric fields
compare with physics of throws (mechanics, EP1)
Experimental Physics IIa - Electric charge, field, dipole
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Electric dipoles

p
A system of two equal and opposite charges q separated by a small distance
L ia called an electric dipole
the electric dipole moment:
-
q
p  qL
p
L
+
q
points from the negative to the
positive charge and has the length
| qL |
+
p
+
Experimental Physics IIa - Electric charge, field, dipole
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Electric dipoles
 
k

E (r )  3 (3 prˆ  cos   p)
r
the field of an electric dipol
Experimental Physics IIa - Electric charge, field, dipole
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Electric dipoles in external electric fields

E
uniform electric field:
  
  p E

p
torque on the dipole

F2
-
q
+

F1

q
work done by electric field, when the dipol rotates:
dW  d   pE sin d
potential energy:

U   pE cos    pE
Experimental Physics IIa - Electric charge, field, dipole
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Electric Dipoles in External Electric Fields
nonuniform electric field:

p
q
+

F1

F2 - q
example: a dipole in the field
of a positive point charge


F2  F1
+
a net force acts
on the dipole
Experimental Physics IIa - Electric charge, field, dipole
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To remember!
 Charges produce electric fields .
 Electric field exerts force on (other) charges.
 Electric field is defined by measuring the force on a test
charge with an infinitely small charge.
 Electric field lines are used to visualize the electric field
 Dipoles have no net charge.
 Dipoles have an electric dipole moment p.
 Electric field of a dipole is proportional p/r3.
 In electric fields a torque may act on dipoles .
Experimental Physics IIa - Electric charge, field, dipole
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