Concept explainers
A uniformly charged filament lies along the x axis between x = a = 1.00 m and x = a + ℓ = 3.00 m as shown in Figure P25.66. The total charge on the filament is 1.60 nC. Calculate successive approximations for the electric potential at the origin by modeling the filament as (a) a single charged particle at x = 2.00 m, (b) two 0.800-nC charged particles at x = 1.5 m and x = 2.5 m, and (c) four 0.400-nC charged particles at x = 1.25 m, x = 1.75 m, x = 2.25 m, and x = 2.75 m. (d) Explain how the results compare with the potential given by the exact expression
(a)
The electric potential due to single charge particle.
Answer to Problem 25.66AP
The electric potential due to single charge particle is
Explanation of Solution
Given info: The total charge on the filament is
Formula to calculate the electric potential due to point change is,
Here,
Substitute
Conclusion:
Therefore, the electric potential due to single charge particle is
(b)
The electric potential due to two charged particles.
Answer to Problem 25.66AP
The electric potential due to two charged particles is
Explanation of Solution
Given info: The charge on two particles is
Formula to calculate the total electric potential tow charge particles is,
Here,
Substitute
Conclusion:
Therefore, the electric potential due to two charged particles is
(c)
The electric potential due to four charged particles.
Answer to Problem 25.66AP
The electric potential due to four charged particles is
Explanation of Solution
Given info: The charge on four particles is
Formula to calculate the total electric potential tow charge particles is,
Here,
Substitute
Conclusion:
Therefore, the electric potential due to four charged particles is
(d)
The comparison between the electric potential due to charged filament and the calculated value of electric potential in part (a), part (b) and part (c).
Answer to Problem 25.66AP
The calculated value of electric potential due to charged filament is
Explanation of Solution
The total charge on the filament is
The given expression of the electric potential is,
Here,
Substitute
The electric potential due to charged filament is
Conclusion:
Therefore, the calculated value of electric potential is
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Chapter 25 Solutions
Physics for Scientists and Engineers (AP Edition)
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