Today 2/20

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Today 2/20

• E-Field and Coulombs Law 18.4-5
• HW 2/20 E Field 1 Due Monday 2/24
• Next weeks lab Electrostatics

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Electric Forces
The net force caused by all the other charges!
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Electric Field
The net Field caused by all the other charges!
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Electric Field E

• A condition of space caused by the presence of
  charges.
• The field has both size and direction. (its a
  vector)
• Far away the field is weak and near charges the
  field is strong.
• A charge placed in an electric field will feel a
  force.
• Charges both cause and react to electric fields

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Force from the Electric Field

• F qE
• Put charge q in an E field and it feels a force F
• This actually serves to define what we mean by
  the E field since we measure E with F and q.
• Note q is NOT the charge that is causing E !!
  (more later)

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Electric Field
Newtons (N)
F is in units of
Coulombs (C)
q is in units of
Newtons/Coulomb (N/C)
So E is in units of
E tells us how many Newtons of force are on q for
every Coulomb of charge in q.
F qE
just like W mg
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Electric Field
E and F are both vectors. How are their
directions related?

• If q is a positive charge, then F points in the
  same direction as E.
• If q is a negative charge, then F points in the
  opposite direction as E.
• This is different than gravity where there is no
  repulsion.

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Example
At the location marked with an x, the electric
field is 2000 N/C and points right. What is the
electric force (size and direction) on a 6 x 10-6
C charge that is placed at the x?
F qE (2000)(6x10-6) 1.2 x 10-2 N (to the
right)
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Example cont.
What if the charge were the same size but
negative?
Same size F 1.2 x 10-2 N (to the left)
What if a charge were placed somewhere else?
F Who Knows?
Must know E at the new location, where q is.
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Example
A charge of -5 x 10-8 C feels a force of 2.5 x
10-1 N to the right. What is the electric field
(magnitude and direction) at the charges
location?
F qE , E 5 x 106 N/C (to the left)
This is the field at the location of q. We know
nothing about the field at other locations.
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Electric Field
Electric fields are caused by other charges in
other locations. It is very important to
separate the charges causing the field from the
one feeling the effects of the field.
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Electric Fields
A positive charge is placed as shown below. What
direction does the electric field point at the x?

A positive charge placed at the x would feel a
force to the right (repulsion), so the electric
field at the x must also points right. For Q
the E field points away from Q.
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Electric Fields
The electric field caused by a positive charges
points away from the positive charge.
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Coulombs Law
The size of E at x is given by
Qs
k 9 x 109 Nm2/C2 r is the distance from Qs to
the x.
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Example
A 2.5 x 10-6 C charge is placed as shown below.
What is the electric field at a point 5 cm to the
right?
Which way does E point?
E kQs /r2 (9 x 109)(2.5 x 10-6) /(5 x
10-2)2 9 x 106 N/C
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Two point charges Q and -Q are fixed in place a
distance 2d apart as shown. What direction is
the electric field at the midpoint between the
charges?
Q
-Q
d
d
Student 2 The electric field is given by
EkQs/r2 so if do the calculation I get Enet
k(Q)/d2 k(-Q)/d2 0 So, the electric field is
zero and has no direction.
What do you think?
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Example
What is the electric field strength at the
location of Q1 due to Q2?
0.20 m
Q1
Q2
Which charge do we care about?
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Example
What is the electric field strength at the
location of Q1 due to Q2?
0.20 m
Q2
Which charge do we care about? How does this
change the problem?
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Example
Note that the minus sign on Q2 only gives
direction of the E field. It does not matter in
the equation.
1350 N/C
Q2 (-6 x 10-9C)
E kQs /r2 (9 x 109)(6 x 10-9) /(0.20)2
1350 N/C
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Many Charge Example (Like HW)
E kQs /r2
Each Square is ro on a side, Q1 -4qo, Q2
2qo, Q3 -6qo (See how this simplifies the
math)
Q1
Find the E field at Q1s location.
Up, (away from Q2)
EQ2,x
Q2
Down, (toward Q3)
EQ3,x
Q3
Add vectors to get
Enet,x
Down at the x