Download 15A Electric Forces and Electric Fields (Notes Phy

Chapter 16
Electric Forces and
Electric Fields
Phy 2054
Lecture Notes
Electric Forces and Electric Fields
Sections
15-01 Properties of Electric Charges
15-02
15-03
15-04
15-05
Insulators and Conductors
Coulomb’s Law
The Electric Field
Electric Field Lines
15-06 Conductors in Electrostatic Equilibrium
15-07 The Millikan Oil-Drop Experiment
15-08 The Van de Graaff Generator
Ch15: Electric Charge and Electric Field (02 of 46)
Properties of Electric Charges
Attraction
Repulsion
Ch15: Electric Charge and Electric Field (03 of 46)
Chapter 15: Electric Forces and Electric Fields
Is it possible for two negative charges to attract each other?
(A) Yes, they always attract.
(B) Yes, they will attract if they are close enough.
(C) Yes, they will attract if one carries a larger charge
than the other.
(D) No, they will never attract.
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Ch15: Electric Charge and Electric Field (04 of 46)
Insulators and Conductors
Charging by Contact
Ch15: Electric Charge and Electric Field (05 of 46)
Insulators and Conductors
Charging by Induction
Connect
Bring
Remove
A
metal
ground
insphere.
ground
charged
a charged
wirewire.
rod.
torod.
sphere.
Ch15: Electric Charge and Electric Field (06 of 46)
Chapter 15: Electric Forces and Electric Fields
How can a negatively charged rod charge an electroscope
positively?
(A) by conduction
(B) by induction
(C) by deduction
(D) It cannot.
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Ch15: Electric Charge and Electric Field (07 of 46)
Chapter 15: Electric Forces and Electric Fields
A neutral atom always has
(A) more neutrons than protons.
(B) more protons than electrons.
(C) the same number of neutrons as protons.
(D) the same number of protons as electrons.
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Ch15: Electric Charge and Electric Field (08 of 46)
Chapter 15: Electric Forces and Electric Fields
A negatively charged rod is brought near one end of an
uncharged metal bar. The end of the metal bar farthest
from the charged rod will be charged
(A) positive.
(B) negative.
(C) neutral.
(D) none of the given answers
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Ch15: Electric Charge and Electric Field (09 of 46)
Coulomb’s Law
Coulomb’s law:
F12
Q1
F21
r
F  F12  F21
Force (N)
Q1Q 2
Fk
r2
Q2
Charge (Q)
Coulombs (C)
1 C = 6.2421 x 1018 e
e = 1.602 x 10-19 C
Distance (m)
Coulomb’s constant (k)
k = 8.988 x 109 Nm2/C2
Ch15: Electric Charge and Electric Field (10 of 46)
Coulomb’s Law
Coulomb’s law:
Q1
r
Q2
Q1Q 2
Fk
r2
1 Q1Q 2
F
4πεo r 2
1
k
4 πεo
2
1
C
12
εo 
 8.85 x 10
Nm 2
4πk
Permittivity of free space
Ch15: Electric Charge and Electric Field (11 of 46)
Chapter 15: Electric Forces and Electric Fields
What are the units of the Coulomb constant k, which
appears in Coulomb's law?
(A) N∙m/C
Q1Q 2
Fk
r2
(B) N/C
(C) N2∙m/C2
Fr 2
k
Q1Q 2
(D) N∙m2/C2
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Ch15: Electric Charge and Electric Field (12 of 46)
Coulomb’s Law
The force is along the line connecting the charges,
and is attractive if the charges are opposite, and
repulsive if they are the same.
Ch15: Electric Charge and Electric Field (13 of 46)
Chapter 15: Electric Forces and Electric Fields
Two charges are separated by a distance d and exert
mutual attractive forces of F on each other. If the charges
are separated by a distance of d/3, what are the new
mutual forces?
(A) F/9
(B) F/3
(C) 3F
(D) 9F
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Ch15: Electric Charge and Electric Field (14 of 46)
Coulomb’s Law
Vector addition review:
Two forces acting
on an object
tail-to-tip method
Parallelogram method
Components method
Ch15: Electric Charge and Electric Field (15 of 46)
Coulomb’s Law
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces on
each charge from every other charge can be calculated
and then added as vectors.
Net force on Q3
F32
Q3
F31
F32
Fnet
Q3
Q2
Q1
F31
Ch15: Electric Charge and Electric Field (16 of 46)
Coulomb’s Law (Problem)
Two charged dust particles exert a force of 0.032 N on
each other. What will be the force if they are moved so
they are only one-eighth as far apart?
Coulomb’s law is an inverse square law.
F  64 0.032 N   2.048 N
Ch15: Electric Charge and Electric Field (17 of 46)
Coulomb’s Law (Problem)
What is the magnitude of the electrical force between two
people 10 m apart if each water molecule in their bodies is
assumed to have a net negative charge of q = 1.6 x 10-19 C?
Assume each body is 45 kg.
45 kg
 2500 mol
0.018 kg/mole


2500 mol 6.02 x 1023 molucules  1.5 x 1027 molecules
mole


Q  1.5 x 1027 molecules 1.6 x 10-19 C / molecules  2.4 x 108 C

Q 2 9.0 x 109 N  m 2 /C2 2.4 x 108 C
Fk

2
r
10 m 2

2
 5.2 x 1024 N
Ch15: Electric Charge and Electric Field (18 of 46)
Coulomb’s Law (Problem)
A person scuffing her feet on a wool rug on a dry day
accumulates a net charge of -42 mC. How many excess
electrons does she get,

- 42 x 10- 6 C
1 electron

 2.622 x 1014 electrons


 - 1.602 x 10-19 C 
By how much does her mass increase?
- 31 kg 

9
.11
x
10
  2.389 x 10 -16 kg
2.622 x 1014 e - 
1
e


Ch15: Electric Charge and Electric Field (19 of 46)
Coulomb’s Law (Problem)
Compare the electric force holding the electron in orbit
(r = 0.53 x 10 l0 m) around the proton nucleus of the
hydrogen atom, with the gravitational force between the
same electron and proton.
What is the ratio of these two forces?
kQ1Q 2
FE
2
kQ1Q 2
r


FG Gm 1m 2 Gm 1m 2
r2

8.988 x 109
N  m 2 /C2



2
19
1.602 x 10
C

6.67 x 10-11 N  m 2 /kg 2 9.11 x 10- 31 kg 1.67 x 10- 27 kg

 2.3 x 1039
Ch15: Electric Charge and Electric Field (20 of 46)
Coulomb’s Law (Problem)
At each corner of a square of
side L there are four point
charges. Determine the force
on the charge 2Q.
2Q
Q
4Q
L
3Q
k 2Q Q k 2Q 4Q
kQ 2
kQ 2
o
2  2 2   4.8284 2
Fx 

cos 45 
2
2
2
L
2L
L
L
2
2
k 2Q 3Q k 2Q 4Q
kQ
kQ
6  2 2   8.8284 2
Fy 

sin 45o 
2
2
2
L
2L
L
L
F2Q 
Fx2  Fy2

kQ 2
10.0625
L2
Ch15: Electric Charge and Electric Field (21 of 46)
Coulomb’s Law (Problem)
Q1
Q2
Q
x
d
A +4.75 mC and a -3.55 mC charge are placed 18.5 cm apart.
Where can a third charge be placed so that it experiences no
net force?
F1  F2
Q1Q
Q 2Q
k
k
2
x2
d  x 
Q2
xd
Q1 - Q 2
x  18.5 cm
3.5 x 10- 6 C
4.7 x 10- 6 C -
3.5 x 10- 6 C
 116 cm
Ch15: Electric Charge and Electric Field (22 of 46)
The Electric Field
The electric field is defined as the force on a test charge
(small positive charge), divided by the charge:
F
E
q
E
E
F
F  qE
F
F  -qE
Ch15: Electric Charge and Electric Field (23 of 46)
The Electric Field
Electric field of a point charge
q

+Q
r
Qq
Fk
r2
Qq
k
2
F
r
E 
q
q
Q
Ek
r2
Ch15: Electric Charge and Electric Field (24 of 46)
Chapter 15: Electric Forces and Electric Fields
At twice the distance from a point charge, the strength of the
electric field
(A) is four times its original value.
(B) is twice its original value.
(C) is one-half its original value.
(D) is one-fourth its original value.
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Ch15: Electric Charge and Electric Field (25 of 46)
The Electric Field
Problem solving in electrostatics:
Draw a diagram; show all charges, with signs,
and electric fields and forces with directions
Calculate forces using Coulomb’s law
Add forces vectorially to get result
Ch15: Electric Charge and Electric Field (26 of 46)
The Electric Field (Problem)
A proton is released in a uniform electric field, and it
experiences an electric force of 3.75 x 10-14 N toward
the south. What are the magnitude and direction of the
electric field?
E
+
F
3.75 x 10 -14 N
F
E


1
9
q 1.602 x 10
C
south
2.34 x 105 N/C (South)
Ch15: Electric Charge and Electric Field (27 of 46)
The Electric Field (Problem)
What are the magnitude and direction of the electric
field at a point midway between a +7.0 mC and a -8.0 mC
charge 8.0 cm apart? Assume no other charges are
nearby.
d
E1
E  E1  E 2

+
q1
kq1
kq 2
E2
E

d 2 d 2
2
2
   


-
q2
4k
4 8.988 x109 N  m/C
- 6 N  8.0 x10- 6 N

E
q1  q 2  
7.0
x10
d2
0.08 m 2

E  8.4 x107 N/C
Ch15: Electric Charge and Electric Field (28 of 46)
The Electric Field (Problem)
E2
P

E1
x
-
-Q
 2Q
d = 12 cm
+
Two point charges, -Q and +2Q, are separated by a distance
of d = 12 cm. The electric field at point P is zero, where is
point P and how far is it from -Q?
Q1
xd
E1  E 2
2Q1 - Q1
kQ1
kQ 2

2
x
x  d 2
Q1
xd
Q 2 - Q1
d
12 cm
x

2 -1
2 -1
x  29 cm
Ch15: Electric Charge and Electric Field (29 of 46)
The Electric Field (Problem)
A proton (m = 1.67 x 10-27 kg) is suspended at rest in a
uniform electric field E. Take into account gravity at the
Earth's surface, and determine E.
FE
+
q
FG
FE  FG
E
qE  mg
mg
E
q

1.67 x 10- 27 kg 9.80 m/s 2
E
1.602 x 10-19 C

E  1.02 x 10- 7 N/C
Ch15: Electric Charge and Electric Field (30 of 46)
Electric Field Lines
The electric field can be represented by field lines. These
lines start on a positive charge and end on a negative
charge.
Ch15: Electric Charge and Electric Field (31 of 46)
Electric Field Lines
The number of field lines starting (ending) on a positive
(negative) charge is proportional to the magnitude of the
charge.
E
The electric field is stronger where the field lines are closer
together.
E
A
B
C
Ch15: Electric Charge and Electric Field (32 of 46)
Chapter 15: Electric Forces and Electric Fields
The electric field shown
E
(A) decreases to the right.
(B) increases down.
(C) increases to the right.
(D) decreases down.
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Ch15: Electric Charge and Electric Field (33 of 46)
Electric Field Lines
Electric field of two charges:
Ch15: Electric Charge and Electric Field (34 of 46)
Electric Field Lines
The electric field between two closely spaced, oppositely
charged parallel plates is constant.
Ch15: Electric Charge and Electric Field (35 of 46)
Electric Field Lines
Summary of field lines:
Field lines start on positive charges and end on negative
charges; the number is proportional to the magnitude of
the charge.
The magnitude of the field is proportional to the density
of the lines.
Field lines indicate the direction of the field; the field is
tangent to the line.
Ch15: Electric Charge and Electric Field (36 of 46)
Chapter 15: Electric Forces and Electric Fields
Electric field lines near positive point charges
(A) circle clockwise.
(B) circle counter-clockwise.
(C) radiate inward.
(D) radiate outward.
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Ch15: Electric Charge and Electric Field (37 of 46)
Conductors in Electrostatic Equilibrium
Ch15: Electric Charge and Electric Field (38 of 46)
Conductors in Electrostatic Equilibrium
The electric field is
perpendicular to the
surface of a conductor
The electric field is zero
inside a conductor
Ch15: Electric Charge and Electric Field (39 of 46)
Chapter 15: Electric Forces and Electric Fields
A cubic block of aluminum rests on a wooden table in a region
where a uniform electric field is directed straight upward. What
can be said concerning the charge on the block's top surface?
(A) The top surface is charged positively.
(B) The top surface is charged negatively.
(C) The top surface is neutral.
(D) The top surface's charge cannot be
determined without further information.
E
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Ch15: Electric Charge and Electric Field (40 of 46)
Chapter 15: Electric Forces and Electric Fields
Materials in which the electrons are bound very loosely to
the nuclei and can move about freely within the material
are referred to as
(A) insulators.
(B) conductors.
(C) semiconductors.
(D) superconductors.
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Ch15: Electric Charge and Electric Field (41 of 46)
Chapter 15: Electric Forces and Electric Fields
A solid block of metal in electrostatic equilibrium is
placed in a uniform electric field. Give a statement
concerning the electric field in the block's interior.
(A) There is no electric field in the block's interior.
(B) The interior field points in a direction opposite to the
exterior field.
(C) The interior field points in a direction that is at right
angles to the exterior field.
(D) The interior points in a direction that is parallel to the
exterior field.
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Ch15: Electric Charge and Electric Field (42 of 46)
The Millikan Oil-Drop Experiment
Ch15: Electric Charge and Electric Field (43 of 46)
The Van de Graaff Generator
Ch15: Electric Charge and Electric Field (44 of 46)
Ch15: Electric Charge and Electric Field (45 of 46)
Conductors in Electrostatic Equilibrium
Charging by induction:
Electrically neutral
When finger is removed
When charged rod is removed
Net positive charge
( on outer surface)
Electric Charge and Electric Field 16