Physics 212 Lecture 2, Slide 1

1
Physics 212 Lecture 2

• Today's Concept
• The Electric Field
• From a point charge
• From a dipole
• From a line of charge

2
Index
Dipole
Preflight 1
Two Charges
TwoNeg
Preflight 2
Three Charges
Rod
Preflight 3
RodQ
Charges on Strings
ArcQ
Preflight 4
Music
Extra 2
Extra 3
Extra 4
Extra 5
3
simulation
You just need to use vector addition. For point
A, they are equal distances and the charges will
just be opposite of each other, so when you add
them together the resulting vector is pointing
up.
We know this because the field always goes into
the negative charge and out the positive.
Opposite charges cancels each other out when
their distances are the same apart at A
4
simulation
The positive charge is pushing it right and the
negative charge is pulling it left, but the
positive charge is much closer than the negative
charge, so it has a stronger impact.
Red is negative, not positive
5
A) Electric fields flow from positive to
negative B) When you add the field vectors from
the positive charges, the sum points upward and
to the right. The field from the negative charge
is in the opposite direction, but it doesn't
cancel out the effects of the two positive
charges because the negative charge is farther
away. C) The combined component of the positive
charges is directly opposite the negative
component therefore canceling each other out.
BACK
6
A) the fields cancel out at A while b is affected
in the same direction by both. B) They are both
equal because they are the same distance away
from the charges. C) A is closer to both lines of
charge while B is very far from the bottom line.
7

• The positive charge points up, and towards the
  left so the resultant vector points to the left.
• In a line of charge the electic field is only
  dependent on the radius, or distance away from
  the line.
• Because there are more positive charges to the
  left than to the right, the repulsive force will
  point up and to the right.

8
Charges on Strings
Two balls of equal mass are suspended from the
ceiling with nonconducting wire. One ball is
given a charge 3q and the other is given a
charge q.
g
q
3q
Which of the following best represents the
equilibrium positions?
q
3q
q
3q
3q
q
(b)
(a)
(c)
9
Charges on Strings
Which best represents the equilibrium position?
q
3q
q
3q
3q
q
(b)
(a)
(c)

• Remember Newtons Third Law!
• F31 -F13

• Can we solve this quantitatively?
• How do we start?

10
Charges on Strings
How do we solve this quantitatively?

• Concept What Principle/Law(s) do we use?

q
3q

• Strategy What are the unknowns?

11
BACK
12
Two Negative Charges
A
B
C
D
BACK
13
Three Charges
Compare the force on the middle charge in the two
cases below.

Case A
2q
q
-q
Case B
2q
q
-2q
14
d
d
2
3
1
Case A
2q
q
-q
There is an easier way !!!!
d
d
2
3
1
Case B
q
-2q
2q
15
Three Charges
Compare the force on the middle charge in the two
cases below.

Case A
2q
q
-q
Case B
q
2q
-2q
BACK
16
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

17
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-

BACK
18
Straight Rod
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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a
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
20
a
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 !!
21
Music 1

• Who is the Artist?
• Marvin Gaye
• Aaron Neville
• Michael Bolton
• Al Green
• Ray Charles

Different.. Mostly covers.. Very good

• Pretty Woman Roy Orbison
• Unchained Melody Righteous Brothers
• Funny How Time Slips Away Willie Nelson
• Ain't No Mountain High Enough Marvin Gaye
• How Can you Mend A Broken Heart Bee Gees
• Take Me To The River Al Green
• Im So Lonesome I Could Cry Hank Williams
• I Can't Get Next To You Temptations
• My Girl Temptations
• Light My Fire Doors

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Ad Lib 2
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Ad Lib 3
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Ad Lib 4
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Ad Lib 5
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