Physics 212 Lecture 2, Slide 1

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Physics 212 Lecture 2
Today's Concept The Electric Field Continuous
Charge Distributions
Note If you registered your clicker last
semester, you do NOT need to register it again
this semester. (You can. but you dont need to).
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Your Comments
The parts of the pre-lecture about taking the
integral of a line of infinite charge were gone
over a bit quickly and i still don't completely
understand how they found the answer.
the integration of infinite lines of charge!
I think just reinforcing the same things would
help me the most. They seem a bit confusing but I
think with enough practice at this point I am
fine.
I would like more of the preflight questions to
be discussed in lecture
One of the homework problems asks us to determine
where the field is zero when there are charges
with differing strengths and signs. I tried doing
it without going through the guided help, and I
wasn't able to get the right answer. I'll try
using the help next, but is there a
straightforward method for solving these types of
problems?
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Coulombs Law (from last time)
If there are more than two charges present, the
total force on any given charge is just the
vector sum of the forces due to each of the other
charges
what exactly each variable stands for
F1
F2,1
F3,1
F4,1
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Electric Field
Why is an electric field calculated assuming a
positive charge would be placed somewhere?
What exactly IS an electrical field?
The electric field E at a point in space is
simply the force per unit charge at that point.
Electric field due to a point charged
particle Superposition
E4
E2
E
Field points toward negative and Away from
positive charges.
E3
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5
Preflight
Lecture is very good. More discussion on dipoles
would be good.
simulation
Because the electric field is defined as the
direction of force exerted on a positive charge,
A would be repelled from the positive Q and
attracted to the negative Q.
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6
Preflight
simulation
B?
4)
The pull left by the negative charge is much
larger than the push right by the positive charge
since the negative charge is much closer.
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7
Preflight
The magnitudes are equal but the directions are
different. No components are cancelled.
1 2 Same
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Electric Field

• Three positive particles are arranged
  horizontally with equal separation. A fourth
  positive particle with three times the charge is
  placed directly above the middle particle. What
  is the direction of the electric field directly
  between the middle particle and the particle with
  charge 3q?

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Electric Field

• Three positive particles are arranged
  horizontally with equal separation. A fourth
  positive particle with three times the charge is
  placed directly above the middle particle.

What is the direction of the force on a
negatively charged particle placed at that point?
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10
Try using our electric field simulation Goofy
demo
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Example
I would like to see a few more examples
involving multiple charges/fields.
q
P
-q
q

• Calculate E at point P.

d
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Two Charges
Two charges q1 and q2 are fixed at points
(-a,0) and (a,0) as shown. Together they produce
an electric field at point (0,d) which is
directed along the negative y-axis.
y
(0,d)
q1
q2
x
(-a,0)
(a,0)

• Which of the following statements is true
• Both charges are negative
• Both charges are positive
• The charges are opposite
• There is not enough information to tell how the
  charges are related

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-
-


-

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Continuous Charge Distributions
I don't understand the whole dq thing and
lambda.
Summation becomes an integral (be careful with
vector nature) Symmetry is often helpful Linear
charge density is often useful
lQ/L dq l dx
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Charge Density
the whole concept of a charge density is still
fuzzy for me.

• Linear (lQ/L) Coulombs/meter
• Surface (s Q/A) Coulombs/meter2
• Volume (r Q/ V) Coulombs/meter3
• Some Geometry
• Sphere
• Cylinder

• What has more net charge?.
• A sphere w/ radius 2 meters and volume charge
  density r 2 C/m3
• A sphere w/ radius 2 meters and surface charge
  density s 2 C/m2
• Both A) and B) have the same net charge.

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16
Preflight
The field vectors cancel out for point A, but
add together for point B.
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ACT
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Straight Rod
REALLY REALLY TOUGH and COMPLICATED versions of
calculating electric fields due to multiple
finite lines of charges. )
A rod carries a total charge of Q, uniformly
distributed over its length. What is the
direction of E at the origin?
A)
E 0
B)
E
C)
E
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Straight Rod Q
A rod carries a total charge of Q, uniformly
distributed over its length and a point charge Q
is located as shown. What is the direction of E
at the origin?
a
A)
E 0
a
B)
E
C)
E
There is no exact cancellation here ! The point
charge Q is at a distance a from origin The rod
has some charge that is gt distance a from origin
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Arc Rod Q
y
An arc carries a total charge of Q, uniformly
distributed over its length and a point charge Q
is located as shown What is the direction of E
at the origin?
-Q
a
A)
E 0
x
a
B)
E
C)
E
There is no exact cancellation here ! The point
charge Q is at a distance a from origin The arc
has all its charge at a distance a from
origin However, most of arc charge gives rise to
field not along 45o line !!
simulation
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Arc Rod Q
I would like it if the professor deals more with
the integrals of electric fields practices. )
y
An arc carries a total charge of Q, uniformly
distributed over its length and a point charge Q
is located as shown Calculate E at the origin!
Q
a
x
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Notes

• Preflight Prelecture 3 due by 600 AM Tuesday
• Homework 1 is due Thursday Jan 29th
• Labs start February 2nd
• Discussion Quiz next week will be on Coulombs
  Law and E
• Homework 2 is due Tuesday February 3rd (600 AM)