Transcript Chapter14

Electric Forces
•
Coulomb’s Law

F1on 2 
q1q2
rˆ
2
4o r
1
F1on2
r
F2on1
q1
r
q2
Group Problems
What is the force (magnitude and direction) on a -10 mC charge
located at x = 4 m from a 5 mC charge at the origin?
Steps: a. Draw quick sketch (labeled with info)
b. Decide on relevant idea/theory/equation and make
correspondence of variables – what is given, what is unknown –
can you solve for unknowns?
c. Do the math – be sure to answer completely and to put units
d. Check answer if at all possible
1.
2.
Repeat the previous problem when the 5 mC charge is located at
x = 1 m and is replaced with a -5 mC charge.
3.
What is the force on a charge Q located at x1 from a charge q
located at x2? Try to get a general expression that works for all
values of the variables.
Superposition of Forces


Fnet   Fi
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Example
Conductors vs Insulators
Semiconductors
Action at a Distance
Group Problems
1. Four charges, all of magnitude Q, lie at
the corners of a square with sides of
length L. If the top two charges are
positive and the bottom two are negative,
what is the direction of the force on a
positive charge q located at the center of
the square?
2. Find the net force on this charge in terms
of the variables given.
Class Problem
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Three charges are arrayed on a line as
Q
-q
Q
shown.
1
2
x
3x
a) Find the force on –q in terms of x.
b) What ratio Q2/Q1 results in F = 0 on –q?
Electric Field
q*
r
q

 F
E
q*
r’
q
1  qq *
E

q *  4 o r 2

q
rˆ  
rˆ
2
 4 o r
E field of point charge
E field - more
• Mapping of E field
• Examples
• Electrostatic field in conductors
the electric field and net charge inside any conductor after
reaching electrostatic equilibrium are zero
the electric field just outside the conducting surface must
be perpendicular to the surface.
Efield mapping
Group Problems
1. Two charges +Q and –Q lie on the y-axis at +L
and –L, respectively. Find the E field at a
distance x along the x-axis. Simplify this in the
case when x>> L.
2. Suppose the two charges in the previous
problem (±Q) lie along the x-axis at ±L,
respectively. Find the E field a distance x
along the x-axis.
3. Harder: simplify this again when x>>L (need
the fact that (1 + )-2 ~ 1-2 for <<1)
Electrophoresis
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Physics
Macromolecular charges
Problems
Modern Methods
- PAGE
- Isoelectric focusing
anode
++++++++
Positive charge
Decreasing pH
Isoelectric point
Negative charge
------------cathode