Transcript PHYS_3342_083011

The GEMS tutoring is in the Conference Center, not Founders
Your first homework assignment is on Mastering Physics. It is due
next Tuesday.
Superposition of electric forces
For point charges in vacuum (or in air) – we can add forces as a vector sum
q
q
Find a force acting on one of the charges from
the other three
q
L
q
Electric field and Electric Forces
Electric field E is the force per unit “test” charge: F=q2E
Coulomb’s law is “exact” only in electrostatics! (source charges do not move)
Charge #2
Three point charges lie at the vertices of an
equilateral triangle as shown. All three
charges have the same magnitude, but
Charge #1 is positive (+q) and Charges #2
and #3 are negative (–q).
The net electric force that Charges #2 and
#3 exert on Charge #1 is in
–q
Charge #1
+q
y
–q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
Charge #3
Some Definitions
• Electric Field—Field set up by an electric charge in the space
surrounding it, which will produce a force on any other charged
particle brought into the field.
• Vector Field—A field that has both magnitude and direction. It is
symbolized by lines; vectors in space.
• Test charge—A small positive charge used to determine the
electric field. It has to be much smaller than the source charge so
that it doesn’t affect the electric field.
• Electric Field Lines—Lines that follow the same direction as the
electric field vector at any point
Electric Field and Electric Forces
But charges are finely balanced in nature:
The number of protons in a 70 kg body = 2×1028
If two such bodies have that charge imbalanced by just
1%, then the repulsion force at the arm length of 0.5 m
would be
(9×109) ((2×1026)(1.6×10-19))2/0.52 ~ 1026 N sufficient to lift a mass of
~ 1026/10 = 1025 kg – on the order of the Earth’s mass!!!
It is the electric forces that make solids “solid” and work in chemical
reactions, etc
Electric field strength – force acting
on the unit charge


F
E
q0
Typical electric field magnitudes
(N/C = V/m)
Michael Faraday (1791-1867). Field vs action-at-a-distance.
In our everyday experiences, we tend to think of a force being exerted only
when contact is made between material bodies, as when we push open a door.
Newton's law of gravitation had already introduced the notion that a force
could act at a distance. But this idea of "action at a distance" deeply troubled
many thinkers. At any moment in time, the earth has to "know"
instantaneously the sun's position and to "feel" the appropriate force. The
phenomenon of electromagnetism demonstrated this apparent action at a
distance even more dramatically. That magnets would act on each other while
separated by empty space is most alluring to children, and to physicists as
well. Like many of his predecessors and contemporaries, Faraday grappled
with this philosophical problem and finally reached the following picture.
He proposed that an electric charge produces around it an electric field of
force. When another charge is introduced into this electric field, the field
acts on this charge, exerting on it a force in accordance with Coulomb's law.
The important point is that this electric field is to be thought of as a separate
entity: The electric field produced by an electric charge exists, regardless of
whether another charge is introduced to feel the effect of the field. Similarly,
one envisages a magnetic field produced by a magnet or an electric current.
Thus, Faraday introduced an intermediary: Two charges do not act "directly"
on each other but they each produce an electric field that, in turn, acts on the
other charge. (From A. Zee, “Fearful Symmetry”)
For non-point charges, we can “divide”
a charged body into point charges


F0
E  lim
q0 0 q0
Electric field of a point charge
E  ke
q
r2
q 
E  ke 2 r
r
magnitude

magnitude and direction
Electric field – vector field, may change from
point to point. Think of wind velocity in the
atmosphere as an example of a vector field
Charge #1
Two point charges and a point P lie at the
vertices of an equilateral triangle as shown.
Both point charges have the same
magnitude q but opposite signs. There is
nothing at point P.
The net electric field that Charges #1 and
#2 produce at point P is in
–q
P
y
+q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
Charge #2
Example: Find the electric field at point P
James Clerk Maxwell (1831-1879). Field concept brings fruit.
Maxwell put it all together in four mathematical statements, known ever since as
Maxwell's equations. The equations specify how the electromagnetic field
varies, in space and in time. Armed finally with the correct equations, Maxwell
was able to go further. In a flash of insight, he made one of those truly amazing
discoveries in physics: the existence of electromagnetic waves. Roughly
speaking, if we have in a region of space an electric field changing in time, then
a magnetic field is produced in the neighboring space. Its very production means
that this magnetic field is also changing in time—and it generates an electric
field. Thus, like a ripple on a pond spreading from a dropped pebble, an
electromagnetic field propagates out in a wave, undulating between electric and
magnetic energy. The value obtained theoretically for the speed of his
electromagnetic wave coincides closely with the measured speed of light! And
thus Maxwell proclaimed that the mysterious phenomenon of light is just a form
of electromagnetic wave. In one stroke, optics as a field of physics was
subsumed under the study of electromagnetism. Maxwell's discovery
demonstrated conclusively the physical reality of the field and its claim to a
separate existence. Indeed, the space around us is literally humming with
packets of electromagnetic field hurrying hither and yon. In recent decades,
physicists have come to the view that all physical reality is to be described in
terms of fields, an idea we will come back to later. It is interesting how this
concept originated in the vague philosophical unease physicists felt with the
action-at-a-distance hypothesis. (From A. Zee, “Fearful Symmetry”)
Maxwell Equations

E 
0
B
t
E j
2
c B 

t  0
E  
B  0
All of the electromagnetism is contained in
Maxwell equations!
“From a long view of the history of mankind … there
can be little doubt that the most significant event of
the 19th century will be judged as Maxwell’s
discovery of the laws of electrodynamics.”
(R.P. Feynman)
Electric E and magnetic B fields are vector fields existing at
each point of space surrounding charges and that can
continuously change in space and time:
Ex ( x, y, z, t ), E y ( x, y, z, t ), Ez ( x, y, z, t )
Bx ( x, y, z, t ), By ( x, y, z, t ), Bz ( x, y, z, t )
We will spend time to study how
(1) E and B are created by charges
(2) Charges are affected by E and B
Forces and fields obey the superposition principle:
Field from a group of particles is a vector sum of fields
from each particle
E  E1  E 2  ...   Ei
i
E x  E1x  E2 x  ...   Eix
i
E y  E1 y  E2 y  ...   Eiy
i
E z  E1z  E2 z  ...   Eiz
i
Electric Field Properties
• A small positive test charge is used to determine the
electric field at a given point
• The electric field is a vector field that can be symbolized
by lines in space called electric field lines
• The electric field is continuous, existing at every point, it
just changes in magnitude with distance from the source
Electric Field Equation
• Electric Field

 F
E
qo

1 qsource
qsource
E
rˆ  ke 2 rˆ
2
4 o r
r
• For a continuous charge distribution


dq
dq
dE  ke 2 rˆ  E  ke  2 rˆ
r
r
Reading assignment : 21.5 – 21.7