In this example, our goal is to calculate the electric field,
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The wire can be divided into small segments each has length
where
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and is the unit vector in the
direction of the vector
. Putting
, Equation (1) becomes:
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(3) |
By using vector a operation, the vector
can be written in terms of position vector
such that:
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(4) |
and the length of can be expressed as a
function of geometric parameters:
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(5) |
The charge of the segment, ,
can be written as:
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(6) |
Subsitution of Equations (4), (5) and (6) into Equation (3) yields:
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(7) |
The total electric field, , is the
integral of electric field
over the wire.
So, the componets of
are found by evaluating the following integrals:
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(8) |
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(9) |
In our program, we will evaluate these integrals numerially.
Integrating a function can be calculated by
Simpson's method.
The approximation to the integral is:
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(10) |
where is a finite length of
. Note that numerical errors can be
reduced by making
smaller.
The Simpson method in Equation (10) is used to solve the integrals
in Equation (8) and (9).
The computer programs in Fortran 90 and C can be found at:
linearCharge.f90 |
linearCharge.c
You can also download an executable visual program file produced by Borland C++ Builder 1.0 from: linearCharge.exe
You can input
and
parameters and the program
plots the 2D-distribution of the electric field vectors,
.
Secreen Shots:
02_1.jpg |
02_2.jpg |
02_3.jpg