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Electric Field
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The direction of the field is taken to
be the direction of the force it would exert on a positive test charge
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Electric Field of Point Charge
The electric field of a point charge can be obtained from Coulomb's law:
The electric field is radially outward from the point charge in all directions
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The electric field from any number of point charges can be obtained from a vector sum of the
individual fields
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This electric field expression can also be obtained by applying Gauss' law
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The direction of the electric field is always directed in
the direction that a positive test charge would be pushed or pulled if placed in the space
surrounding the source charge
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For any given location, the arrows point in the direction
of the electric field and their length is proportional to the strength of the electric field at
that location
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Note that the lengths
of the arrows are longer when closer to the source charge and shorter when further
from the source charge
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Rather than draw countless vector arrows
in the space surrounding a source charge, it is perhaps more useful to draw a pattern of
several lines that extend between infinity and the source charge
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As such, the lines are directed away
from positively charged source charges and toward negatively charged source charges
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An electric field line pattern could
include an infinite number of lines
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The
presence of a few lines around a charge is typically sufficient to convey the nature of the
electric field in the space surrounding the lines
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The conventions are simply established in order that electric field line patterns
communicate the greatest amount of information about the nature of the electric field
surrounding a charged object
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Objects with greater charge create stronger electric fields
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This
convention is depicted in the diagram below
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Consider the object shown at
the right
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These cross-sections represent regions of space
closer to and further from the source charge
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Based on the convention
concerning line density, one would reason that the electric field is greatest at locations
closest to the surface of the charge and least at locations further from the surface of the
charge
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A second rule for drawing electric field lines involves drawing the lines of force
perpendicular to the surfaces of objects at the locations where the lines connect to
object's surfaces
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The electric force, and thus the electric field, is always directed perpendicular to
the surface of an object
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This would lead to the occurrence of an electric current within the
object; this is never observed in static electricity
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This occurs when drawing electric field lines
for configurations of two or more charges as discussed in the section below
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Electric field
lines should never cross
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If electric field lines were ever allowed to cross each other at a given
location, then you might be able to imagine the results
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If the lines cross each other at a given location, then there must be two distinctly
different values of electric field with their own individual direction at that given
location
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Every single location in space has its own electric
field strength and direction associated with it
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Electric Field Lines for Configurations of Two or More
Charges
In the examples above, we've seen electric field lines for the space surrounding single
point charges
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Suppose that there are two positive charges - charge A (QA) and charge B (QB) - in a given
region of space
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At any given location
surrounding the charges, the strength of the electric field can be calculated using the
expression kQ/d2
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The results of these calculations are illustrated in the
diagram below with electric field vectors (EA and EB) drawn at a variety of locations
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Since electric field is a vector, the usual operations that apply to vectors can be applied
to electric field
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This is shown in the diagram below
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If more locations are selected and the process of drawing E A, EB and Enet is repeated, then
the electric field strength and direction at a multitude of locations will be known
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) Ultimately, the electric field lines
surrounding the configuration of our two charges would begin to emerge
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This is depicted in the diagram below
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The construction of electric field lines in this manner is a tedious and cumbersome task
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Whatever the method used to
determine the electric field line patterns for a configuration of charges, the general idea
is that the pattern is the resultant of the patterns for the individual charges within the
configuration
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In each of the above diagrams, the individual source charges in the configuration
possess the same amount of charge
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Subsequently, the pattern is
symmetrical in nature and the number of lines emanating from a source charge or
extending towards a source charge is the same
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If the quantity of charge on
a source charge is not identical, the pattern will take on an asymmetric nature, as one of
the source charges will have a greater ability to alter the electrical nature of the
surrounding space
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After plotting the electric field line patterns for a variety of charge configurations, the
general patterns for other configurations can be predicted
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These principles are described (or redescribed) in the list below
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Electric field lines never cross each other
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At locations where electric field lines meet the surface of an object, the lines are
perpendicular to the surface