Physics 213 General Physics Lecture 2 0
Jan 20, 2016
Physics 213General Physics
Lecture 2
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Last Meeting: Electric Charge, Conductors/Insulators
Today: Static Charges, Conductors, Coulomb’s Law, Electric Forces, Electric Field
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Demo
Glass, Silk, Amber, Fur, Tape conduction/induction
Comb and PaperPivoting PlankVan de Graaff Generator
Van de GraaffGenerator
Charge is transferred to the dome by means of a rotating belt
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Charging by Conduction
A charged object (the rod) is placed in contact with another object (the sphere)
Some electrons on the rod can move to the sphere
When the rod is removed, the sphere is left with a charge
The object being charged is always left with a charge having the same sign as the object doing the charging
Charging by Induction
• When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded
• A neutral sphere has equal number of electrons and protons
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Polarization
In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge
In the presence of a charged object, these centers may separate slightly This results in more positive charge on
one side of the molecule than on the other side surface of the insulator
This realignment of charge on the surface of an insulator is known as polarization
A charged comb attracts bits of paper due to polarization of the paper
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Vector Nature of Electric Forces
Two point charges are separated by a distance r
The like charges produce a repulsive force between them
The force on q1 is equal in magnitude and opposite in direction to the force on q2
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Vector Nature of Forces, cont.
Two point charges are separated by a distance r
The unlike charges produce a attractive force between them
The force on q1 is equal in magnitude and opposite in direction to the force on q2
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Vector Nature of Electric Forces
Magnitude of the force
In the direction of
The precise Coulomb’s law
1 22
| || |q qF k
r
1 212 2
q qF k
r
12r 12r
1 212 122 12ˆ ˆ ( is a unit vector)r
q qF k r
r
21 12r r
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Unit Vectors
A unit vector is a dimensionless vector with a magnitude of exactly 1.
Unit vectors are used to specify a direction Reference: Serway and Vuille, 8th ed.
Chapter 3.
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Unit Vectors, cont.
The symbols
represent unit vectors They form a set of
mutually perpendicular vectors
Right-hand convention
ˆˆ ˆ, ,i j and k
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Unit Vectors in Vector Notation
Ax is the same as Ax and Ay is the same as Ay etc.
The complete vector can be expressed as
i
j
ˆ ˆ ˆx y zA A A A i j k
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Adding Vectors Using Unit Vectors
Using R = A + BThen
and so Rx = Ax + Bx and Ry = Ay + By
ˆ ˆ ˆ ˆ
ˆ ˆ
x y x y
x x y y
x y
A A B B
A B A B
R i j i j
R i j
R R R
2 2 1tan yx y
x
RR R R
R
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Vector Nature of Forces, cont. Two point charges are
separated by a distance r The unlike charges
produce an attractive force between them
The force on q1 is equal in magnitude and opposite in direction to the force on q2
pair)reaction -(action ˆˆ 21221
2112221
12 rr
qqkFr
r
qqkF
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Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown. Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge at the upper right corner?a. A
b. Bc. Cd. De. The net force on that charge is zero
Answer: b
Question:
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20
3
1
2
Answer:4
Consider first the force from 1 on 4.
We will now do the forces from the other charges on 4.We can add up all three force vectors to determine the net force on 4.
21
3
1
2
Answer:
2
1 2
2
2 2
3 2
2
3 3 2
2
3 3 2
1 3
2 3
in the direction D2
1cos 45
2 2
1sin 45
2 20
0
The answer is B.
x
y
x
y
x x x
y y y
QF k
a
QF k
aQQ
F ka
QF F k
a
QF F k
a
F F F
F F F
Superposition Principle
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22
221
rmm
GF
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Q
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Faraday introduced electric field and electric field lines which are said to exist in the region of space around a charged object. When another charged object enters this electric field, the field exerts a force on the second charged object
2| ( ) |
qE r k
r
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Coulombs force and electric fields.
12221
12 rrqq
kF
12221
12 rrqq
kF
1221
1 rrq
kE
q1q2 qtest
q3q4
Superposition Principle
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Direction of Electric Field
The electric field produced by a negative charge is directed toward the charge A positive test
charge would be attracted to the negative source charge
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Direction of Electric Field, cont
The electric field produced by a positive charge is directed away from the charge A positive test
charge would be repelled from the positive source charge
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An electron traveling horizontally enters a region where a uniform electric field is directed upward.What is the direction of the force exerted on the electron once it has entered the field?
(a) to the left
(b) to the right
(c) upward
(d) Downward
(e) out of the page, toward the reader
Answer: d
Question:
Rules for Drawing Electric Field Lines1. The lines for a group of charges must begin on
positive charges and end on negative chargesIn the case of an excess of charge, some lines will begin or
end infinitely far away
2. The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge
3. No two field lines can cross each other4. The net number of lines at infinite distance is
proportional to the net charge in the system.
Electric Field Line Patterns
Point charge
The lines radiate equally in all directions
For a positive source charge, the lines will radiate outward
Electric Field Line Patterns
For a negative source charge, the lines will point inward
Electric Field Line Patterns
An electric dipole consists of two equal and opposite charges
The high density of lines between the charges indicates the strong electric field in this region
Electric Field Line Patterns
Two equal but like point charges
At a great distance from the charges, the field would be approximately that of a single charge of 2q
The bulging out of the field lines between the charges indicates the repulsion between the charges
The low density of field lines between the charges indicates a weak field in this region
Electric Field Patterns
Unequal and unlike charges
Note that two lines leave the +2q charge for each line that terminates on -q