Transcript Lec-2_Strachan

0
Physics 213
General Physics
Lecture 2

Last Meeting: Electric Charge,
Conductors/Insulators
 Today:
Static Charges,
Conductors, Coulomb’s Law,
Electric Forces, Electric Field
2
Demo
Glass, Silk, Amber, Fur, Tape
conduction/induction
 Comb and Paper
 Pivoting Plank
 Van de Graaff Generator

3
Van de Graaff
Generator
Charge is transferred to the
dome by means of a rotating
belt
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
5
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
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
7
8

9
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
10
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
11
Vector Nature of Electric Forces

Magnitude of the force
|q1||q2|
Fk 2
r


In the direction of r12
qq
F12 k 122
r


r12
r21  r12
The precise Coulomb’s law
q
q
1
2
ˆ
ˆ
F

k
r
r
i
s
a
u
n
i
t
v
e
c
t
o
r
)
1
2
2(
1
2
21
r
12
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.

13
Unit Vectors, cont.

The symbols
iˆ, ˆj, and kˆ
represent unit vectors
 They form a set of
mutually
perpendicular vectors
 Right-hand
convention
14
Unit Vectors in Vector Notation
Ax is the same as
Ax î and Ay is the
same as Ay ĵ etc.
 The complete
vector can be
expressed as

ˆ
ˆ
ˆ
A

A
i

A
j

A
k
x
y
z
15
Adding Vectors Using Unit Vectors
Using R = A + B
 Then
R
 Aˆ
iAˆ
j  Bˆ
iBˆ
j


x
y


x
y


ˆ
ˆ
R
A

B
i

A

B

x
x
y
y j
R
R
R
x
y

and so Rx = Ax + Bx and Ry = Ay + By
R
R

R

R

t
a
n
R
x
2
x
2
y

1y
16
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
q
q
q
q
1
2
1
2
ˆ
ˆ
F

k
r


F


k
r
(act
rea
p
12
12
21
21
2
2
r
r
17
Question:
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. B
c. C
d. D
e. The net force on that charge is zero
Answer: b
18
19
Answer:
1
4
Consider first the force from 1 on 4.
3
2
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.
20
1
Answer:
Q 2
F1 x  k
a2
Q 2
F2 y  k
a2
QQ
F3  k
2a


2
 in th e d ir e c tio n D
3
4
2
Q2 1
F3 x  F3 c o s 4 5  k
2a2 2
Q2 1
F 3 y  F 3 s in 4 5  k
2a2 2
F x  F1 x  F 3 x  0
F y  F2 y  F3 y  0
T h e a n s w e r is B .
Superposition Principle
21
m1m2
F  G 2
r
22
Q
23
q
| E ( r ) | k 2
r
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
24
25
Coulombs force and electric fields.

q1q2
F12  k 2 r̂12
r

q1q2
F12  k 2 r̂12
r

q1
E1  k 2 r̂12
r

q2
qtest
Superposition Principle
q4
q3
q1
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
27
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
28
Question:
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
29
Rules for Drawing Electric Field
Lines
1. The lines for a group of charges must begin on
positive charges and end on negative charges
In 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 other
4. 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