Download Lecture 10 - Eunil Won

Eunil Won, Dept. of Physics, Korea Univ
Ch10 Introduction to Electricity
and Magnetism
This is what it looks
like inside your cellular
phone
: it is all about electricity
and magnetism
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Eunil Won, Dept. of Physics, Korea Univ
Electric Charges and Forces
Electromagnetism: the combination of
electrical and magnetic phenomena
Charges with the same electrical sign repel each
other, and charges with opposite electrical signs
attract each other
conductors: some of electrons in materials can
move rather freely
ex) metals, human body
insulators: none of electrons in materials can
move freely
ex) plastic, glass
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Eunil Won, Dept. of Physics, Korea Univ
Coulomb’s Law
The electrostatic force of attraction or repulsion between two charged
particles (q1 and q2) has the magnitude
(Coulomb’s law)
k: electrostatic constant
Unit of charge: C (Coulomb)
One Coulomb is the amount of charge
that is transferred through the cross
section of a wire in 1 second when
there is a current of 1 Ampere
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Eunil Won, Dept. of Physics, Korea Univ
Coulomb’s Law
k: electrostatic constant and is usually written as 1/4πε0
Then Coulomb’s law becomes
ε0 permittivity constant:
A shell of uniform charge attracts or repels a charged particle that is
outside the shell as if all the shell’s charge were concentrated at its center
If a charged particle is located inside a shell of uniform charge, there is
no net electrostatic force on the particle from the shell
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Eunil Won, Dept. of Physics, Korea Univ
Charge is Quantized
Benjamin Franklin thought that electric charge was a continuous
fluid but...
Experiments show that any charge q that can be detected written
as:
e, the elementary charge has the (small) value:
Conservation of charge: the net charge of any
isolated system cannot change
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Eunil Won, Dept. of Physics, Korea Univ
Electrostatic Force >> Gravitational Force
FC = 10 Fg
39
FC =
Fg = G
1
q p qe
4πε 0 r 2
mp me
r2
−19 2
(
1
.
60
×
10
)
−8
9
=
8
.
2
×
10
N
= 8.99 ×10
−10 2
(0.53 ×10 )
−21
−27
(
9
.
11
×
10
)(
1
.
67
×
10
)
−11
−47
= 6.67 ×10
=
3
.
6
×
10
N
−10 2
(0.53×10 )
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Eunil Won, Dept. of Physics, Korea Univ
Example 10.1
If all the positive and negative charges in 1 g of water could
be separated, they would total 5.35 x 104 C and -5.35 x 104
C, respectively. Calculate the force between such charges
when separated by 1.0 m.
Negative sign: attractive force
This is an extremely large force
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Eunil Won, Dept. of Physics, Korea Univ
The Electric Field
We define the electric field at point due to the charged object:
SI unit for the electric field:
N/C (newton per Coulomb)
Electric field lines: extend
away from positive charge
and toward negative charge
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Eunil Won, Dept. of Physics, Korea Univ
The Electric Field Due to a Point Charge
The magnitude of the electrostatic force on q0 due to a point
charge q:
The magnitude of the electric field due to a point charge q:
Net force from the n point charges:
Net electric field due to n point charges:
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Eunil Won, Dept. of Physics, Korea Univ
The Electric Field Due to an Electric Dipole
electric dipole: two charged particles of magnitude q
but of opposite sign, separated by a distance d
electric field at point P:
note:
p = qd : electric dipole
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Eunil Won, Dept. of Physics, Korea Univ
A Dipole in an Electric Field
A molecule of water is an electric dipole: the
electric dipole points from oxygen to the hydrogen side
Let’s consider a dipole in an electric field (uniform):
net force on the dipole is zero
but there is torque acting on the dipole
the magnitude of each force : F = qE
assume x is the position of the center of mass of the dipole
system:
Generalizing the above we get:
Note: torque is clockwise (reducing the angle θ) : we put minus
sign with the torque (useful for the discussion with the potential
energy)
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Eunil Won, Dept. of Physics, Korea Univ
A Dipole in an Electric Field
Potential energy of an electric dipole at any angle θ:
o
(we choose the potential energy to be zero when the angle θ is 90 )
the integral becomes:
or
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Eunil Won, Dept. of Physics, Korea Univ
Electric Potential Energy
Newton’s law for the gravitation force and Coulomb’s law for the electrostatic
force are mathematically identical
The electrostatic force is also a conservative force : we can assign an electric
potential energy U to the system
(path independent)
Convenience, we take U to be zero (all particles are infinitely apart each
i
other)
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Eunil Won, Dept. of Physics, Korea Univ
Electric Potential
The potential energy per unit charge at a point : called the electric
potential (V)
(path independent)
SI unit: J/C or 1 Volt (V)
The electric potential difference between any two points i and f:
ex) Home AC power has: 220 V
We can now adopt a new unit for electric field:
ex) energy required to move electron
through 1 Volt potential difference:
ex) energy required to move 1 kg by
height of 1 m:
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Eunil Won, Dept. of Physics, Korea Univ
Equipotential Surfaces
Adjacent points that have the same electric
potential form an equipotential surface: no
work is need for any path on the equipotential
surface
ex) equipotential surface for uniform electric field: plane
equipotential surface produced by a point charge: concentric
spheres
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Eunil Won, Dept. of Physics, Korea Univ
Calculating the Potential from the Field
differential work done on a particle by a force
(positive test charge q moves from i to f ):
0
the total work becomes:
in other words:
finally we choose the initial electric potential is zero
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Eunil Won, Dept. of Physics, Korea Univ
Potential Due to a Point Charge
First we evaluate the dot product:
the angle θ is zero (from the figure), and we take r=R from
the initial and r=infinity to the final position
we know that
the integral becomes:
note: positively charged
particle produces a
positive electric potential
For a group of point
charges:
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Eunil Won, Dept. of Physics, Korea Univ
Example 10.2
Calculate the speed of an electron accelerated by the 20,000 V potential difference
found in the CRT. The mass of electron is 9.11x10-31 kg.
KE = 12 mv 2 = qV
1/2
⎛ 2(1.6 ×10 C)(2.0 ×10 V) ⎞
⎛ 2qV ⎞
⎟⎟
v=⎜
⎟ = ⎜⎜
-31
9.11×10 kg
⎝ m ⎠
⎠
⎝
= (7.03 ×1015 m 2 /s 2 )1/2 = 8.4 ×107 m/s
1/2
-19
4
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Eunil Won, Dept. of Physics, Korea Univ
Definition of Current
the free electrons in an isolated wire: in random
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motion at speeds of 10 m/s but no net current
through the wire
when the wire is connected, there is a net transport
of charge : electric current
charge carrier: electron
(but we define the direction of the current with +q)
electric current:
SI unit : 1 ampere = 1A = 1
coulomb per second = 1 C/s
total charge passes
through in a time interval
electric charge conservation requires
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Eunil Won, Dept. of Physics, Korea Univ
Current Density
current density:
current per unit area with the direction defined by the current
itself
drift speed: electrons drift with a drift speed when there is a current in a
conductor
ex) vd ~ 10-5 or 10-4 m/s in copper conductors
n : number of charge carriers per unit volume
A : wire’s cross sectional area
L : length of the wire under consideration
Extending this as a vector form:
For positive (negative) carrier, current density and the velocity have same (opposite)
direction
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Eunil Won, Dept. of Physics, Korea Univ
Resistance and Resistivity
We determine the electric resistance between any two points of a conductor
by applying a potential difference
SI unit: 1 ohm = 1 Ω = 1 volt per ampere = 1 V/A
: a conductor provides a specified resistance is called a resistor
resistivity:
SI unit:
in a vector form,
conductivity:
From the figure on the left:
and
: macroscopic quantities (practically useful)
: microscopic quantities (useful in studying
fundamental electrical properties of materials)
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Eunil Won, Dept. of Physics, Korea Univ
Ohm’s Law
: an assertion that the current through a device is always directly proportional to the
potential difference
historically, it is called law but it is an (obeying Ohm’s law)
assertion that may or may not be true
Ohm’s law can be expressed
as:
or
(I-V curve from a semiconducting pn
junction diode)
(microscopic)
A Microscopic View of Ohm’s Law
e: electric charge of an electron
m: mass of electron
E: electric field applied
τ : average time between
collisions
From
we get
finally we get
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Eunil Won, Dept. of Physics, Korea Univ
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Eunil Won, Dept. of Physics, Korea Univ
Example 10.3
How many electrons move through a pocket calculator during one hour of use?
q = It
q = (0.3 ×10 A)(1 hr)
-3
= (0.3 ×10 C/s)(3600 s) = 1.08C
-3
1
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1.08C ×
= 6.75 ×10
-19
1.6 ×10 C
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