(d) For comparison purposes, calculate the potential (in V) given by the exact expression (Round your answer to at least three significant figures.) V = ur Find the percentage difference between your result for part (a) (single particle model) and the exact value. | Vexact - Vpart (a) Vexact x 100% = % Find the percentage difference between your result for part (c) (4 particle model) and the exact value.

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The figure below shows a thin, uniformly charged filament lying on the positive x-axis. Its left end is a = 1.00 m from the origin, and its right end is a + { = 5.00 m from the origin. The total charge on
the filament is Q = 2.40 nC. Calculate successive approximations for the electrical potential (in V) at the origin by modeling the filament in the following ways.
P
(a) as a single charged particle at x = 3.00 m (Round your answer to at least three significant figures.)
V
(b) as two charged particles at x = 2.00 m and x = 4.00 m, each with a charge of 1.20 nC, half of the total charge of the filament (Round your answer to at least three significant figures.)
V
(c) as four charged particles at x = 1.50 m, x = 2.50 m, x = 3.50 m, and x = 4.50 m, each with a charge 0.600 nC, one-fourth of the total charge of the filament (Round your answer to at least
three significant figures.)
V
(d) For comparison purposes, calculate the potential (in V) given by the exact expression (Round your answer to at least three significant figures.)
{ + a
V =
u-
V
Find the percentage difference between your result for part (a) (single particle model) and the exact value.
Vexact - Vpart (a)
x 100% =
Vexact
Find the percentage difference between your result for part (c) (4 particle model) and the exact value.
Vexact - Vpart (c)
x 100% =
%
V
exact
Transcribed Image Text:The figure below shows a thin, uniformly charged filament lying on the positive x-axis. Its left end is a = 1.00 m from the origin, and its right end is a + { = 5.00 m from the origin. The total charge on the filament is Q = 2.40 nC. Calculate successive approximations for the electrical potential (in V) at the origin by modeling the filament in the following ways. P (a) as a single charged particle at x = 3.00 m (Round your answer to at least three significant figures.) V (b) as two charged particles at x = 2.00 m and x = 4.00 m, each with a charge of 1.20 nC, half of the total charge of the filament (Round your answer to at least three significant figures.) V (c) as four charged particles at x = 1.50 m, x = 2.50 m, x = 3.50 m, and x = 4.50 m, each with a charge 0.600 nC, one-fourth of the total charge of the filament (Round your answer to at least three significant figures.) V (d) For comparison purposes, calculate the potential (in V) given by the exact expression (Round your answer to at least three significant figures.) { + a V = u- V Find the percentage difference between your result for part (a) (single particle model) and the exact value. Vexact - Vpart (a) x 100% = Vexact Find the percentage difference between your result for part (c) (4 particle model) and the exact value. Vexact - Vpart (c) x 100% = % V exact
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