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MasteringPhysics: Assignment Print View
PSS 26.2: The Field Trip
Learning Goal:
To practice ProblemSolving Strategy 26.2 for problems involving the electric
field due to continuous charge distributions.
A straight wire of length
has a positive charge
distributed along its length. Find the magnitude
of the electric field due to the wire at a point located a distance
from one end of the wire along
the line extending from the wire.
MODEL:
Model the distribution as a simple
shape, such as a line of charge or a disk of
charge. Assume the charge is uniformly
distributed.
VISUALIZE:
For the pictorial
representation:
1.
Draw a picture and establish a
coordinate system.
2.
Identify the point P at which you
want to calculate the electric field.
3.
Divide the total charge
into
small pieces of charge
using
shapes for which you already know how to determine
. This is often, but not always, a
division into point charges.
4.
Draw the electric field vector at P for one or two small pieces of charge. This will help you
identify distances and angles that need to be calculated.
5.
Look for symmetries in the charge distribution that simplify the field. You may conclude
that some components of
are zero.
SOLVE:
The mathematical representation is
.
■
Use superposition to form an algebraic expression for each of the three components of
at
point P. (Note that one or more components may be zero.)
■
Let the
coordinates of the point remain as variables.
■
Replace the small charge
with an equivalent expression involving a charge density and
a coordinate, such as
, that describes the shape of charge
.
This is the critical step in
making the transition from a sum to an integral
because you need a coordinate to serve as
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the integration variable.
■
Express all angles and distances in terms of the coordinates.
■
Let the sum become an integral. The integration will be over the coordinate variable that is
related to
. The integration limits for this variable will depend on your choice of
coordinate system. Carry out the integration and simplify the result as much as possible.
ASSESS:
Check that your result is consistent with any limits for which you know what the field
should be.
Start by making simplifying assumptions appropriate for the situation.
Part A
The wire can be modeled as a
line of charge
if you assume which of the following?
A.
The diameter of the cross section is constant throughout the wire.
B.
The diameter of the cross section is much smaller than the length of the wire.
C.
The diameter of the cross section has the same order of magnitude as the length of the wire.
D.
The cross section has a circular shape.
E.
The cross section has a highly symmetrical, though not necessarily circular, shape.
Enter the letters of all the correct answers in alphabetical order. Do not use commas. For instance,
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This note was uploaded on 09/22/2009 for the course PEP 112 taught by Professor Whittaker during the Spring '07 term at Stevens.
 Spring '07
 Whittaker

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