Transcript Electricity and Magnetism - Physics2-Quasar

Electricity and Magnetism
 Electric forces hold atoms and
molecules together.
 Electricity controls our thinking, feeling,
muscles and metabolic processes.
 Electricity and magnetism underpin
much of our current technology (e.g.
computers).
 Electricity and magnetism are linked
on a fundamental level.
Electric Charges
• Evidence for electric charges is everywhere, e.g.
– static electricity.
– lightning.
• Objects may become charged by contact and
frictional forces.
• Benjamin Franklin (1700’s) discovered that there are
two types of charges:
– positive charge.
– negative charge.
• Franklin also discovered that like charges repel and
unlike charges attract one another.
• Electric charge is
– quantized (Millikan)
– conserved (Franklin)
Quantum of Electric Charge
• Electric charge is quantized. The
smallest possible unit is the charge
on one electron or one proton:
e = ±1.602 x 10-19 Coulombs
• No smaller charge has ever been
detected in an experiment.
Electric Charges in Atoms
• Atoms consist of a nucleus
containing positively
charged protons.
• The nucleus of an atom is
surrounded by an equal
number of negatively
charged electrons.
• The net charge on an atom
is zero.
• An atom may gain or lose
electrons, becoming an ion
with a net negative or
positive charge.
• Polar molecules have zero
net charge but their charges
are unevenly distributed in
space (e.g. water).
Nuclear diameter ~ 10-15 m
(femtometer)
Atomic diameter ~ 10-9 m
(nanometer)
Classes of Materials
• CONDUCTORS are materials in which
charges may move freely (e.g. copper).
• INSULATORS are materials in which charges
cannot move freely (e.g. glass).
• SEMICONDUCTORS are materials in which
charges may move under some conditions
(e.g. silicon).
Charges and the Earth
• The earth acts as a near-infinite source
or sink of charges, and therefore its net
charge cannot easily be changed.
• Any conductor in contact with the earth
is said to be GROUNDED and cannot
receive a net charge. (principle of
lightning rod)
Induced Charge
• Charged objects brought close to a conductor may
cause charge to redistribute (polarize the conductor).
• If a polarized conductor is momentarily grounded,
charge will be transferred to/from the earth, and it
may be left with a net charge (by INDUCTION).
• Objects may be charged by
– conduction (requires contact with another
charged object.
– induction (requires no contact with another
charged object).
Electric Force and Coulomb’s Law
• If two point charges q1 and q2 are separated
by a distance r, the magnitude of the electric
force Fe between them is:
Fe  k
q1 q2
r
2
where k = 8.99 x 10 9 Nm2/C2 is the Coulomb
constant, q1 and q2 are in Coulombs (C), r is
in meters (m) and Fe is in Newtons (N).
Electric Force Vector
• The force on a point charge q1 exerted
by another point charge q2 separated
by a distance r21 is:



kq1q2
F12  2 rˆ21
F21   F12
r21
where rˆ21 is a unit vecto r along the axis
joining q2 and q1.
Principle of Superposition
• For a system of N charges q1, q2, q3, …, qN,
the resultant force F1 on q1 exerted by
charges q2, q3, …, qN is:
 


F1  F12  F13    F1N
• Each charge may be considered to exert a
force on q1 that is independent of the other
charges present.
Example #1
• One kg of hydrogen is 1000
grams, and has therefore 1000
times Avagadro's number of
electrons.
How many
coulomb's of
• Q = 1000* NA * e
charge is
• where e = 1.602 x10-19 C,
contained in the
and NA = Avogadro's number =
electrons of one
6.02 x 1023
kg of hydrogen?
• Q = -4.82 x 107 C
Example #2
Consider one gram of
hydrogen gas which
has been separated
into its electrons and
protons. The electrons
are placed on Earth's
north pole and the
protons are placed on
Earth's south pole.
What is the magnitude
of the force the
electrons feel due to the
presence of the
protons?
• Remember that one gram of
H gas has one mole
(Avagadro's number) of
hydrogen atoms.
• The force between the (+)
and (-) charges is given by
Coulomb's law where the
separation distance r is
2*6.37E6 m.
• F = 5.14E5 N
Example #3
Two charges
feel a
repulsive
force of 96
(N). What is
the force if
the
separation, r,
is quadrupled.
Solution:
kq1q2
F1 
2
r1
kq1q2
1 kq1q2
F2 

2
2
( 4r1 )
16 r1
1
F2 
F1
16
Solution:
Example #4
Three charges are
placed along a 10mm line as shown in
the diagram. Find
the force felt by the
proton if it is at the
midpoint.
2e
p
F  F1  F2
kpe 2kpe
F  2  2
r
r
kpe
F   2
r
e
Example #5
Imagine 3 charges,
separated in an
equilateral triangle
as shown above,
with L = 2.0 cm, q =
1.0 nC. What is the
magnitude and
direction of the force
felt by the upper
charge?
L
Example #5
(con’t)
Solution:
2kq2
Fx  F1x  F2 x  2 sin 30(1  1)
L
Fx  0
L
2kq2 cos 30(1  1)
Fy 
L2
4kq2
Fy 
cos 30
2
L
More Sample Problems
Find the force experienced by the
central charge. Where red dots
represent an electron and green dots
represents protons. The equilateral
triangle below has sides of length
1fm.
Find the force experienced by the
central charge. Where red dots
represent an electron and green dots
represents protons. The sides of the
square are1fm long.