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Electric Fields
March 13-15
Today
• HW Tonight - Online (Electrostatics Problems 2.5)
> Net Charge; Coulomb's Law
• Tomorrow - Short Quiz: Charges, Coulomb's Law
• Electric Fields
> see Notes online: Intro to Electrostatics
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Electric Fields
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Question: Why does the Electrostatic Force have the characteristics that
we observe? E.g., why does the Force increase as Q increases? Why does
the Force vary inversely with distance?
Answer: Michael Faraday's ELECTRIC FIELD
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Electric Fields
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Classical Definition: If a small positive "test" charge q0 is placed at a point
in space, and it is observed to experience an Electrostatic Force FE, then at
that there exists an Electric Field, E, such that
E = FE
q0
The direction of the Electric Field is defined as the direction of the
Electrostatic Force on the positive charge.
> This implies that a positive charge will experience an FE in the same
direction as E; a negative charge will experience an FE in the opposite
direction as E.
The unit for Electric Field is N/C.
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Electric Fields
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Example 1: A proton is observed to experience an Electrostatic Force to
your left; the force has a magnitude of 4.8 E-15 N. What is the magnitude
and direction of the Electric Field at the location of this proton?
Example 2: An electron is placed in a uniform Electric Field, with a
magnitude of 5 E5 N/C, and it is directed downwards. What is the
magnitude and direction of the Electrostatic Force on this electron?
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Electric Fields
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Electric Field Lines
We can represent the Electric Field in diagrams with arrows
(pointing in the direction of E). The relative strength of the
Electric Field will be shown by the density of the Field lines
(i.e., how closely spaced they are); the closer together the lines,
the stronger the field at that point.
lines spaced far apart will
indicate a weak E field
here, the tightly packed lines
represent a strong E field
Notice the field lines are parallel and
equally spaced; this implies that the E
field in this region is Uniform (constant)
If you were to put a small positive charge
(red circle) in this E field, it will feel a
Force in the direction of the field (green
arrow). A small negative charge (purple
circle) would feel a force opposite the
direction of the field (black arrow).
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Electric Fields
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Electric Field Due to a "Point" Charge:
For a given charge Q that is at a point in space, it is surrounded by a
spherical Electric Field. The magnitude of this field depends on the size of
the charge, and the distance from the charge. We can calculate this
Electric Field as
E = kQ
R2
where k = 9 E9 Nm2/C2, and R is the distance from the charge.
• Note: this can be derived from Coulomb's Law
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Electric Fields
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Example 1: What is the magnitude and direction of the Electric field a
distance of 0.25 m from a Van de Graaff generator dome that has a net
charge of -8 E-6 C?
Example 2: What is the strength of the Electric field a distance of 3 E-10 m
from a Carbon nucleus, which contains 6 protons and 6 neutrons? What is
the Electrostatic Force on an electron located at that point?
Example 3: A balloon is rubbed on a wool sweater, and a detector measures
an Electric field with a magnitude of 270 N/C when placed a distance of
0.10 m from the balloon. What is the amount of net charge on the balloon?
What is the number of charges associated with this net charge?
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Electric Fields
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E-field due to Q: Diagrams
We can represent the Electric field around a charge Q with a diagram,
integrating the concepts of Electric Field Lines.
The E-field vectors will be drawn according to a few basic rules:
1.
E-field vectors point away from a positive charge and towards a
negative charge;
2.
E-field lines/vectors can NEVER touch or cross each other;
3.
The number of E-field lines indicate the size of the charge (more lines
= stronger field).
Why?
CP Physics
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Recall that the direction of the E-field is the direction of the force on
a positive charge. A + charge will be repelled from a + charge (so Efields go away from +), and attracted to a - charge (so E-fields go
towards a - charge).
2.
If the E-field lines touch/cross, that implies that a charge at a certain
point in space could feel a force in multiple directions; this is
impossible, as the force is always parallel to the E-field.
3.
Recall that the density of the E-field lines indicates its magnitude; if
you draw more lines around a charge, this requires the lines to be
more densely packed, indicating a stronger E-field.
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Electric Fields
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E-field Diagrams
+
E-field near a Positive charge
-
E-field near a Negative charge
Notice in the diagrams above:
• When you are close to the charge (R is small) the E-field lines are close
together (indicating a stronger field ⇒ stronger Force)
• As you get farther away from the charge, the lines spread out (weaker
field ⇒ weaker Force)
> This is why the Force is stronger when charges are closer together;
the Fields have a greater magnitude when you are near the charge
• The number of E-field lines in the diagram above indicate the amount of
charge; more lines = more charge
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Electric Fields
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What if there are multiple charges?
We can diagram any Electric Field, for any number of charges, by using
the rules that govern E-fields and E-field lines:
1.
Away from +, Towards -
2.
E-field lines point in the direction of the Force on a + test charge
3.
The density of the lines indicates the relative strength of E
4.
The number of lines indicates the relative size of the charge
For multiple charges, we end up with E-fields that contain lines that curve
and bend as a result of the sum of two Force vectors. Some examples are
shown below:
Electric Dipole: + and - charge of equal size;
arrows indicate the direction of E. Note that, for
all points equidistant from the + and -, the E-field
is Horizontal, from + to -.
two + charges of equal size. Notice that, at the
center, E = 0! Also, for all points on the vertical
line that bisects the charges, the E-field is
vertical (excluding the exact center point). The
diagram is identical for - charges, except the
arrows point to the charges
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Electric Fields
CP Physics
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