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Experimental Physics IIa - Electric charge, field, dipole 1
Experimental Physics EP2a
Thermodynamics & Electricity
– Electric charge –Conductors, Coulomb’s law
https://bloch.physgeo.uni-leipzig.de/amr/
Experimental Physics IIa - Electric charge, field, dipole 2
Electric chargeAir
Human Hands
Asbestos
Glass
Human Hair
Mica
Nylon
Wool
Lead
Silk
Aluminum
Paper
Cotton
Steel
Wood
Rubber balloon
Hard rubber
Nickel, Copper
Brass, Silver
Gold, Platinum
Sulfur
Celluloid
Silicon
Teflon
+
-
Benjamin FranklinJanuary 17, 1706 Boston
April 17, 1790 Philadelphia
+ -
-
+ +
-
e = 1.602177 ´ 10-19 C
-e
+e
Charge is conserved.
Experimental Physics IIa - Electric charge, field, dipole 3
Conductors and insulators
+ + + + + +
+++++
++++
+
++
--
-
---
---
---
++
++
+
++
+++
++
--- -
--
-
--
-
- -
+ + + + + + --
---
--
--
-
-
-+
++
+
+
+
+ +
++++-
-- -
-
-
-
--
-
- -
++
++
+
++
+++
++
Experimental Physics IIa - Electric charge, field, dipole 4
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.
2,122,1
212,1 r̂
rqkqF =
!22,1
212,1 r
qqkF =
1 22,1r!
229 /CmN109875.8 ×´=k
( ) 104 -= pek
Experimental Physics IIa - Electric charge, field, dipole 5
Some examples
e = 1.6 ´ 10-19 Cmp = 1.67 ´ 10-27 kgme = 9.11 ´ 10-31 kgG = 6.67 ´ 10-11 N m2 kg-2
?-g
e
FF
nC11 =q nC21 -=q
nC11 =qm103.5 11-´=r
?-eF ?-a
Experimental Physics IIa - Electric charge, field, dipole 6
To remember!
Ø Unlike charges attract one another, like charges repel.
Ø Charge is conserved.
Ø Charge is quantized – integer number of electronic charge.
Ø Conductors are materials in which electrons move freely.
Ø In insulator electrons do not move freely.
Ø 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 calledthe Coulomb constant.
Electric field
-321 FFFF ++=+
-
q0+3F
F!
2F
1F
Experimental Physics IIa - Electric charge, field, dipole 7
00/lim
0
qFEq ®
=
•q0 is a test charge(i.e. q0 is small enoughto not alter the electric field)• q0 is positive
131/1 -- ×××= AsmkgCN mV /1=
Electric field
PiPi
iPi rrkqE ,2,
, ˆ=
Coulombs law:
åå ==i
PiPi
i
iPiP r
rkqEE ,2,
, ˆ
-
PiE ,
iq
Pir ,!
P
net electric field, due to a distribution of point charges
electric field, due to charge qi at point P
Experimental Physics IIa - Electric charge, field, dipole 8
Electric field lines
Øelectric field lines (also lines of force) show thedirection of the force exerted on a positive testcharge
Øthe electric field lines point radially away frompositive charges and towards negative charges
Øthe density (spacing) of the lines isproportional to the electric field strenght at that point
Øfield lines do not cross
Øthe number of lines leaving or entering a charge is proportional to the magnitude of thecharge
Øelectric field lines begin on positive charges (orinfinity) and end on negative charges (orinfinity)
+
Experimental Physics IIa - Electric charge, field, dipole 9
monopole2 opposite charges2 equal chargesequal charges, but different magnitude)opposite charges with different magnitudes
Electric field lines
Experimental Physics IIa - Electric charge, field, dipole 10
Motion of a Point Charge in the Electric Field
Emq
mF
a ==å!
example: electron in uniform electric field
CkNEx /1=
- 0v!
e
smv x /102 6,0 ×=
meE
mF
a xx
-==
E
x
xx
avv
x2
2,0
2 -=D cm
eEmv
x x 14.12
2,0 ==D0=xv
How far can it travel until it is momentarily stopped?
the rest is mechanics…
Experimental Physics IIa - Electric charge, field, dipole 11
Motion of point-like charges in electric fields
compare with physics of throws (mechanics, EP1)
Experimental Physics IIa - Electric charge, field, dipole 12
Electric dipoles
+-L
p!
Lqp = q+q-
A system of two equal and opposite charges q separated by a small distance L ia called an electric dipole
the electric dipole moment:
points from the negative to thepositive charge and has the lengthp || Lq
++
-p
Experimental Physics IIa - Electric charge, field, dipole 13
Electric dipoles
)cosˆ3()( 3 prprkrE !""
-×= Jthe field of an electric dipol
Experimental Physics IIa - Electric charge, field, dipole 14
Electric dipoles in external electric fields
+
-p!
Q
q+
q-2F!
1F!E
!
Ep!!!
´=ttorque on the dipole
QQ=Q= dpEddW sintwork done by electric field, when the dipol rotates:
potential energy:
EppEU!!
-=Q-= cos
uniform electric field:
Experimental Physics IIa - Electric charge, field, dipole 15
Electric Dipoles in External Electric Fields nonuniform electric field:
+
-p!
q+
q-
+
1F!
2F!
12 FF!!
>
a net force actson the dipole
example: a dipole in the fieldof a positive point charge
Experimental Physics IIa - Electric charge, field, dipole 16
To remember!
Ø Charges produce electric fields .
Ø Electric field exerts force on (other) charges.
Ø Electric field is defined by measuring the force on a test charge with an infinitely small charge.
Ø Electric field lines are used to visualize the electric field
Ø Dipoles have no net charge.
Ø Dipoles have an electric dipole moment p.
Ø Electric field of a dipole is proportional p/r3.
Ø In electric fields a torque may act on dipoles .
Experimental Physics IIa - Electric charge, field, dipole 17