chapter 21: electric charge and electric...
Post on 21-Mar-2021
10 Views
Preview:
TRANSCRIPT
p212c21: 1
Chapter 21: Electric Charge and Electric FieldElectric Charge
Ancient Greeks ~ 600 BC Static electricity: electric charge via friction (see also fig 21.1)
(Attempted) pith ball demonstration:2 kinds of properties
2 objects with same property repel each other2 objects with different properties attract each otherboth properties are always created together
Benjamin Franklin:kinds of charges are positive and negativeby convention, negative charge associated with amber
Conservation of Charge: The algebraic sum of all the electric charges in any closed system is constant.
p212c21: 2
Conductors and Insulators
(Objects are usually “charged” by moving electric charge around, rather than creating or destroying charge.)
Conductor:
charge passes easily through the material
=> conductors contain charges which are free to move
Insulator:
charge cannot move (easily) through material
Semiconductor:
transition between insulator and conductor, usually of interest because of exotic electrical properties
p212c21: 3
Charging by induction (see also fig 21.6).−−−−
+ −+ − + −
−−−−
+ + +
−−−−
+ + +
++ +
Electrical Force on Neutral Insulators: Induced Polarization (see fig 21.7, n.a. )
−−−−
+ −+ −+ −+ −+ −
+ −+ −+ −+ −+ −+ −
+ −+ −+ −+ −+ −+ −
+ −
p212c21: 4
Quantization and Conservation of ChargeMicroscopic structure of matter: Atoms (see fig 21.4)
Nucleusmost of masspositive chargecomposed of protons (each has charge = +e) and neutrons (no electric charge)
“orbiting” electrons (each has charge = −e)Atoms tend to be charge neutralcharge quantized: e = 1.6x10-19 C
Charge transfer usually in the form of addition or removal of electrons.
p212c21: 5
Coulomb’s LawA description of the interaction between two (point) chargesThe magnitude of the Force exerted by one charge on the other
is proportional to the magnitude of each of the chargesis inversely proportional to the square of the distance between the chargesacts along a line connecting the charges
2
29
2
29
02 10910988.8
41
CmN
CmNk
rQqkF ⋅×≈⋅×===
πε
Unit of charge is the Coulomb, a new type of quantity.
How big is 1 coulomb?
p212c21: 6
Another form of Coulomb’s Law
the force exerted by Q (“source charge”) on q (“test charge”)
q toQ from distance,
q toQ from r,unit vectoˆ
qon Force
ˆ2
=
==
=
r
rF
rrQqkF
ˆ r
F
Q
q
r
p212c21: 7
rrQqkF ˆ2=
ˆ r
F
Q
q
r
Coulomb’s Law: the force exerted by Q on qElectric Charge and Electric Field (cont’d)
∑=
++=
++=
i ii
i rr
qQk
rr
qQkrr
qQk
FFF
ˆ
ˆˆ
2
222
212
1
1
21
r21F
Q1
q
r1
ˆ r 1
2F
Q2ˆ r 2
F
For several Sources
p212c21: 8
•Analyze geometry/draw diagram
•calculate magnitude of each contribution
•calculate components of each contribution
•add contributions as vectors (add component by component)
Fi = kQi q
ri2
A charge q = 5.0 nC is at the origin. A charge Q1 = 2.0 nC is located 2cm to the right on the x axis and and Q2 = −3.0 nC is located 4 cm to the right on the x axis. What is the net force on q?
p212c21: 9
.3m
.3m
.4m
Q1 = 2.0 µC
Q2 = 2.0 µC
q = 4.0 µC
Geometry
Magnitudes
Components
Net Force
p212c21: 10
Example: Compare the electric repulsion of two electrons to theirgravitational attraction
F=k ∣Qq∣r2
versus F=G Mmr 2
p212c21: 11
Electric Field and Electric forcesElectric field is a “disturbance” in space resulting from the presence of (source) charge, which exerts a force on a (test) charge.
ˆ r
Q
P
r
ˆ r
qPFPE
/)at ()at (
≡
Q
q
r )at () o(
qEqqnF
≡
ˆ r
F
Q
q
r
Force of interaction Source charge creates a disturbance in space
Test charge “senses” the disturbance in space
p212c21: 12
2
2
P toQ from distance,
P toQ from r,unit vectoˆ
Pat Field
ˆ
rQkE
r
rE
rrQkE
=
=
==
=
ˆ r
Q
P
r
E
p212c21: 13
r2
Q1r1
ˆ r 1
Q2ˆ r 2
For several Sources
∑=
++=
++=
i ii
i rrQk
rrQkr
rQk
EEE
ˆ
ˆˆ
2
222
212
1
1
21
Force Law: F = qE
2E
E
1E
p212c21: 14
Elementary Electric Field Examples:What is the electric field 30 cm from a +4nC charge?
When a 100 volt battery is connected across two parallel conducting plates 1 cm apart, the resulting charge configuration produces a nearly uniform electric field of magnitude E = 1.00E4 N/C.
Compare the electric force on an electron in this field with its weight.
What is the acceleration of the electron?
The electron is released from rest at the top plate. What is the final speed of the electron as it hits the second plate?How long does it take the electron to travel this distance?
p212c21: 15
Electric Field Calculations
•Analyze geometry/draw diagramElectric Field Contributions are directed away from positive charges, toward negative charges
•calculate magnitude of each contribution
•calculate components of each contribution
•add contributions as vectors (add component by component)
E i=k ∣Qi∣ri
2
p212c21: 16
a
x
+Q
−Q
Geometry
Magnitudes
Components
Net Force
a
Electric Dipole: two equal size(Q), opposite sign charges separated by a distance (l = 2a).Determine the electric field on the x-axis
p212c21: 17
a
x
+Q
−Q
a
( )
( )3
2322
2322
20
xpk
axpk
axaQkE
E
ax
y
x
− →
+−=
+−=
=
>>
Field of an electric dipole
p212c21: 18
a
x
Geometry
Magnitudes
Components
a
Line of charge: uniform line of charge (charge Q, l = 2a oriented along y-axis).Determine the electric field on the x-axissee also animation http://phys23p.sl.psu.edu/phys_anim/EM/E_line_of_charge.avi
y
dQ=λdy
2222
222
22
cos
cossin
22
yxx
yxdyk
EddE
yxdyk
rdQkEd
yxrrx
ry
aQ
ady
QdQ
x
++=
=
+==
+=
==
==
λ
θ
λ
θθ
λ
p212c21: 19
Add Components
( )
rkE
axxkE
axxQkE
axxkQ
axxak
yxdyk
dEE
r
x
x
ay
ay
xx
λ
λ
λ
λ
2 :charge of line infinite
,2
,
2
2
2222
2322
charge all
=
<<≈
>>≈
+=
+=
+=
=
∫
∫=
−=
p212c21: 20
Next: infinite sheet of charge is composed of of a series of infinite lines of charges
Look carefully at related textbook examples of a ring of charge, and a disk of charge.
p212c21: 21
sheet of charge composed of a series of infinite lines of chargeσ = charge per area
Electric Field due to an infinite sheet of charge
z
y
Geometry
Magnitudes
Components
2222
22
22
2
cos
22
cossin
yzy
yzdzk
EddE
yzdzk
rkEd
yzrry
rz
dz
y
++=
=
+==
+=
==
=
σ
θ
σλ
θθ
σλ
θ
p212c21: 22
Add Components
!field! electric uniform4
12
222
2
arctan12
2
00
22
charge all
==
=
−−=
=
+=
=
∞
−∞=
∞=
−∞=∫
∫
πεεσ
σπππσ
σ
σ
k
kk
yz
yyk
yzydzk
dEE
z
z
z
yy
z
y
θ
p212c21: 23
Interaction of an electric dipole with an electric fielddipole in a uniform electric field
x
y
z−q
−ql
F=qE
F=− qE
Ep
pElqE
FlFlRHRFr
F
z
iii
i
×=
==
+=
×==
=
∑∑
∑
τ
θθ
θθτ
ττ
sinsin
sin2
sin2
!dipole ofcenter about torque
0
p
F = F = qE
θ
p212c21: 24
Work done rotating dipole in an electric fieldwatch directions of τ, θ an dθ
x
y
z
θl
EppEU
UpEpE
dpEW
dpEddW
⋅−=−=
∆−=−=
−=
−==
∫
θθ
θθ
θθ
θθθτθ
θ
cos)(
coscos
sin
sin
12
2
1p
dθ
p212c21: 25
“Lines of Force”
Electric Field Lines: a means of visualizing the electric field=A line in space always tangent to the electric field at each point in spaceconcentration give indication of field strengthdirection give direction of electric field•start on positive charges, end on negative charges•electric field lines never cross
see figure 21.26, http://phys23p.sl.psu.edu/simulations/physlets/em_fieldplot.html
p212c21: 26
+ + + + + + + + + + + + + +
− − − − − − − − − − − − − −
top related