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Two long, straight copper pipes, each of radius a, are
Chapter 7, Problem 41P(choose chapter or problem)
Problem 41P
Two long, straight copper pipes, each of radius a, are held a distance 2d apart (see Fig. 7.50). One is at potential V0, the other at −V0. The space surrounding the pipes is filled with weakly conducting material of conductivity σ. Find the current per unit length that flows from one pipe to the other. [Hint: Refer to Prob. 3.12.]
Figure 7.50
Reference prob 3.12
Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V0, the other at −V0 (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob. 2.52.]
Questions & Answers
QUESTION:
Problem 41P
Two long, straight copper pipes, each of radius a, are held a distance 2d apart (see Fig. 7.50). One is at potential V0, the other at −V0. The space surrounding the pipes is filled with weakly conducting material of conductivity σ. Find the current per unit length that flows from one pipe to the other. [Hint: Refer to Prob. 3.12.]
Figure 7.50
Reference prob 3.12
Two long, straight copper pipes, each of radius R, are held a distance 2d apart. One is at potential V0, the other at −V0 (Fig. 3.16). Find the potential everywhere. [Hint: Exploit the result of Prob. 2.52.]
ANSWER:
Step 1 of 4
We have to find the current per unit length that flows from one copper pipe to the other, each of radius and held at a distance apart.
To solve this problem, let us begin by solving a different problem of two parallel wires carrying charges and as shown in figure below.
The electric field and the potential due to one wire is,
where, is the distance from the line charge to a point
which is at a potential
and are the distances from the line charge and to the
point () respectively
Therefore, the potential due to the combination of two wires is,
where, is distance from the origin to line charge.